REFERENCES
G. W. (Pete) Stewart
This is my bibtex reference base. It is available by anonymous ftp
at
thales.cs.umd.edu
in the directory
pub/references
It is also available from netlib. In using it, keep in mind the
following points.
SCOPE
The reference base is a combination of my personal reference
base and a number of others. It includes (at least in part)
1. The bibliography from Introduction to Matrix Computations
by G. W. Stewart.
2. The bibliography from Matrix Perturbation Theory by
G. W. Stewart and J.-G. Sun.
3. Ake Bjorck's bibliography on least squares.
4. The bibliography from Matrix Computations by G. H. Golub
and C. Van Loan.
5. P. C. Hansen's bibliography on rank-revealing decompositions.
UPDATES
The reference base on thales will be updated from time to time, and
items can disappear. For example, I will generally remove techreports
as I find them published in journals. If you use this base in a
\bibliography command, save your bbl files.
CITATION KEYS
A citation key is divided into two fields : separated
by a colon. The author field is constructed as follows. If there is
only one author, the first four letters of his or her last name are
used to form the field (but only one letter each from prefixes; e.g.
van de Geign becomes vdge). If there are two authors the first two
letters in their last names are used. If there are three authors the
first two letters of the first are used with one letter from each of
the second and third. If their are four, one letter from each is
used. Cave: these conventions are not cast in iron.
NAMES
Names appear in the order they appear in the reference, and entries
are alphabetized by the first name to appear. To keep bibtex from
becoming confused, only initials of given names are used.
Speaking of alphabetization, between some entries you will find
curious clusters of two letters--e.g. -ac- -ad-. I use them to
position myself within the reference base when I am inserting items.
I strongly recommend that you adopt some such convention if you plan
to build a large reference base.
KEYWORDS
Each entry has a keyword field, labeled kwds. The program bibsrch
(see below) will search the file for matches in a user specified
combination of conjunctions, disjunctions, and negations. The user
can also specify the author. The program getkey dumps the keywords
on the standard output. To get an alphabetized list of all key words
from the file ref.bib try
getkey ref | sort -uf > keywords
The choice of key words is a highly personal matter, and my choices
suffer from the additional handicap that they were made on the fly as
the reference base grew. In the matter of general subject
categories, I tend to list the most specific. Thus, if a paper is
classified as numerical linear algebra (abbreviated nla), it is not
also classified as numerical analysis (na). Combinations of key
words are especially tricky. For example, the key phrase 'Lanczos
algorithm' is seldom combined with the key word 'sparse', since the
main application of the Lanczos algorithm is to sparse matrices.
Fortunately, bibsrch is flexible enough to pick out entries with
either key word, or both.
I have used a number of abbreviations to keep the kwds field to a
manageable size. Here they are.
cs : computer science
csd : CS decomposition
eig : eigenvalue problems
eriv : errors in variables
geig : generalized eigenvalue problems
ginv : generalized inverse
gsvd : generalized singular value decomposition
iter : iterative methods
la : linear algebra
lsq : least squares
math : mathematics
lud : LU decomposition
na : numerical analysis
nla : numerical linear algebra
nlop : nonlinear equations and optimization
nllsq : nonlinear least squares
prll : parallel computations
pert : perturbation theory
qrd : QR decomposition
regr : regression
stat : statistics
svd : singular value decomposition
The program getkey also prints out these correspondences in the
appropriate places. (They are actually key words in the last article
of the base; take a look.)
DISCLAIMERS
Anyone who has had to read my papers or books knows that as a
proofreader I am at the bottom of the heap. This reference base is
no exception. Do not use the references in a paper, unless you have
checked them out for yourself (actually sound scholarly practice
requires that you never make an indirect reference without giving the
secondary source). Naturally, I am interested in hearing about any
errors you may find.
BIBSRCH
The programs bibsrch and getkey may be generated from the file
bibsrch.tar, available along with this reference base. Simply place
bibsearch.tar in the directory where you want the directory
containing the programs. Then
tar xf bibsearch.tar
cd bibsearch
more README
and you will be told what to do next.
Pete Stewart
-aa-
@article{aase:71,
author = "J. O. Aasen",
year = "1971",
title = "On the Reduction of a Symmetric Matrix to Tridiagonal Form",
journal = "BIT",
volume = "11",
pages = "233-242",
kwds = "nla, symmetric matrix, tridiagonal matrix"
}
-ab-
@article{abde:71,
author = "N. N. Abdelmalek",
year = "1971",
title = "Roundoff Error Analysis for {Gram-Schmidt} Method and
Solution of Linear Least Squares Problems, BIT {\bf 11}, 345--368.",
journal = "BIT",
volume = "11",
pages = "345--368",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "rounding error ,Gram-Schmidt algorithm, qrd"
}
@article{abde:74,
author = "N. N. Abdelmalek",
year = "1974",
title = "On the Solution of Least Squares Problems and Pseudo-Inverses",
journal = "Computing",
volume = "13",
pages = "215--228",
kwds = "la, pert, lsq, ginv"
}
-ac- -ad-
@inproceedings{adgs:91,
author = "G. Adams and M. F. Griffin and G. W. Stewart",
year = "1991",
title = "Direction-of-Arrival Estimation Using the Rank-Revealing
{URV}~Decomposition",
booktitle = "Proceedings of the IEEE International Conference on
Acoustics, Speech and Signal Processing",
editor = "",
pages = "",
publisher = "IEEE",
address = "Washington, DC",
note = "To appear.",
kwds = "nla, rank determination, direction of arrival, urvd"
}
@article{ascr:84,
author = "L. Adams and T. Crockett",
year = "1984",
title = "Modelling Algorithm Execution Time on Processor Arrays",
journal = "{IEEE} Computer",
volume = "17",
pages = "38--43",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll"
}
@article{adam:85,
author = "L. Adams",
year = "1985",
title = "{m}-step Preconditioned Conjugate Gradient Methods",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "6",
pages = "452--463",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning"
}
-af-
@article{afri:56,
author = "S. N. Afriat",
year = "1956",
title = "On the Latent Vectors and Characteristic Values of
Products of Pairs of Symmetric Idempotents",
journal = "Quarterly Journal of Mathematics",
volume = "7",
pages = "76-78",
kwds = "la, eig, projection"
}
@article{afri:57,
author = "S. N. Afriat",
year = "1957",
title = "Orthogonal and Oblique Projectors and the Characteristics of Pairs
of Vector Spaces",
journal = "Proceedings of the Cambridge Philosophical Society",
volume = "53",
pages = "800-816",
kwds = "la, eig, projection, canonical angles"
}
-ag- -ah-
@book{ahhu:74,
author = "A. V. Aho and J. E. Hopcroft and J. D. Ullman",
year = "1974",
title = "The Design and Analysis of Computer Algorithms",
publisher = "Addison-Wesley",
address = "Reading, Massachusetts",
kwds = "algorithms, complexity, book"
}
-ai-
@article{aitk:34,
author = "A. C. Aitken",
year = "1934",
title = "On Least Squares and Linear Combinations of Observations",
journal = "Proceedings of the Royal Society of Edinburgh",
volume = "55",
pages = "42-47",
kwds = "la, stat, lsq, regr"
}
-aj- -ak- -al-
@phdthesis{alba:84,
author = "M. Al-Baali",
year = "1984",
title = "Methods for Nonlinear Least Squares",
school = "University of Dundee",
adress = "Department of Mathematical Sciences",
note = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{alfl:85,
author = "M. Al-Baali and R. Fletcher",
year = "1985",
title = "Variational Methods for Non-linear Least Squares",
journal = "J. of the Operational Research Society",
volume = "36",
pages = "405--421",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{albfl:86,
author = "M. Al-Baali and R. Fletcher",
year = "1986",
title = "An Efficient Line Search for Nonlinear Least-squares",
journal = "J. Opt. Theory Appl.",
volume = "48",
pages = "359--377",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@book{albe:72,
author = "A. Albert",
year = "1972",
title = "Regression and the Moore-Penrose Pseudoinverse",
publisher = "Academic Press",
address = "New York",
kwds = "book, la, stat, regr, ginv"
}
@article{alpp:88,
author = "S. T. Alexander and C.-T. Pan and R. J. Plemmons",
year = "1988",
title = "Analysis of a recursive Least Squares Hyperbolic
Rotation Algorithm for Signal Processing",
journal = "Linear Algebra and Its Applications",
volume = "98",
pages = "3-40",
kwds = "nla, lsq, updating, hyperbolic transformation, signal processing"
}
@article{allg:73,
author = "E.L. Allgower",
year = "1973",
title = "Exact Inverses of Certain Band Matrices",
journal = "Numerische Mathematik",
volume = "21",
pages = "279--284",
note = "Cited in \cite{govl:89}.",
kwds = "la, inverse matrix, band matrix"
}
@article{alma:85,
author = "G. S. Almas",
year = "1985",
title = "Overview of Parallel Computing",
journal = "Parallel Computing",
volume = "2",
pages = "191-203",
kwds = "prll, architecture"
}
@article{altm:61,
author = "N. Altman",
year = "1961",
title = "An Iterative Method for Eigenvalues and Eigenvectors
of Matrices",
journal = "Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.",
volume = "9",
pages = "639--644, 727--732, 751--755",
kwds = "nla, eig, sparse"
}
@article{alva:90,
author = "F. L. Alvarado",
year = "1990",
title = "Manipulating and Visualization of Sparse Matrices",
journal = "ORSA Journal on Computing",
volume = "2",
pages = "186--207",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "sparse, software"
}
-am-
@article{amir:56,
author = "A. R. Amir-Mo\'ez",
year = "1956",
title = "Extremal Properties of Eigenvalues of a {Hermitian}
Transformation and the Singular Values of the Sum
and Product of Linear Transformations",
journal = "Duke Mathematical Journal",
volume = "23",
pages = "463--476",
kwds = "la, pert, eig, symmetric matrix"
}
@article{amgr:88,
author = "G. S. Ammar and W. B. Gragg",
year = "1988",
title = "Superfast Solution of Real Positive Definite
Toeplitz Systems",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "9",
pages = "61--76",
kwds = "nla, fast algorithm, linear system, Toeplitz matrix"
}
@article{amgr:91,
author = "G. S. Ammar and W. B. Gragg",
year = "1991",
title = "{$O(n^2)$} Reduction Algorithms for the Construction
of a Band Matrix from Spectral Data",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "426--431",
kwds = "nla, eig, inverse eigenvalue problem"
}
-an-
@article{ande:74,
author = "A. H. Andersen",
year = "1974",
title = "Multidimensional Contigency Tables",
journal = "Scand.\ J.\ Statist",
volume = "1",
pages = "115-127",
kwds = "stat, contingency table, categorical data"
}
@book{abbd:92,
author = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and
J. Dongarra and J. Du Croz and A. Greenbaum and
S. Hammarling and A. McKenney and S. Ostrouchov and
D. Sorensen",
year = "1992",
title = "{LAPACK} Users' Guide, Release 1.0",
publisher = "SIAM",
address = "Philadelphia",
note = "To appear.",
kwds = "book, nla, software"
}
@article{anos:77,
author = "D. H. Anderson and M. R. Osborne",
year = "1977",
title = "Discrete, Nonlinear Approximation Problems in
Polyhedral Norms",
journal = "Numerische Mathematik",
volume = "28",
pages = "157-170",
kwds = "nlop"
}
@article{anka:75,
author = "N. Anderson and I. Karasalo",
year = "1975",
title = "On Computing Bounds for the Least Singular Value of a Triangular
Matrix",
journal = "BIT",
volume = "15",
pages = "1--4",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "pert, rank determination, svd"
}
@article{anlo:73,
author = "P. Anderson and G. Loizou",
year = "1973",
title = "On the Quadratic Convergence of an Algorithm that Diagonalizes
a Complex Symmetric Matrix",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "12",
pages = "261--271",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, symmetric matrix, complex matrix, Jacobi-like"
}
@article{anlo:76,
author = "P. Anderson and G. Loizou",
year = "1976",
title = "A {J}acobi-Type Method for Complex Symmetric Matrices
({H}andbook)",
journal = "Numerische Mathematik",
volume = "25",
pages = "347--363",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, symmetric matrix, complex matrix, Jacobi-like"
}
@article{ande:76,
author = "T. W. Anderson",
year = "1976",
title = "Estimation of Linear Functional Relationships: Approximate
Distributions and Connections with Simultaneous Equations in
Econometrics ",
journal = "Journal of the Royal Statistical Society",
volume = "38",
pages = "1-31",
kwds = "stat, regr, eriv, functional model"
}
@article{ande:84,
author = "T. W. Anderson",
year = "1984",
title = "Estimating Linear Statistical Relationships",
journal = "Annals of Statistics",
volume = "12",
pages = "1-45",
kwds = "stat, regr, eriv, functional model"
}
@article{anou:87,
author = "T. W. Anderson and I. Olkin and L. G. Underhill",
year = "1987",
title = "Generation of Random Orthogonal Matrices",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "8",
pages = "625--629",
note = "Cited in \cite{govl:89}.",
kwds = "nla, random matrix, orthogonal matrix"
}
@article{ando:89,
author = "T. Ando",
year = "1989",
title = "Majorization, Doubly Stochastic Matrices, and Comparison
of Eigenvalues.",
journal = "Linear Algebra and Its Applications",
volume = "118",
pages = "163--248",
kwds = "la, eig, majorization, doubly stochastic matrix"
}
@techreport{ancl:91,
author = "A. L. Andrew and K. W. E. Chu and P. Lancaster",
year = "1991",
title = "Derivatives of Eigenvalues and Eigenvectors
of Matrix Functions",
institution = "Department of Mathematics and Statistics,
University of Calgary",
type = "Research Paper",
number = "171",
kwds = "la, pert, eig"
}
@article{ansc:83,
author = "G. Andrews and F. B. Schneider",
year = "1983",
title = "Concepts and Notations for Concurrent Programming",
journal = "{ACM} Computing Surveys",
volume = "15",
pages = "1--43",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll"
}
@article{anetal:87,
author = "M. Annoratone and E. Arnould and T. Gross and H. T. Kung
and O. Menzicioglu and J. A. Webb",
year = "1987",
title = "The WARP Computer: Architecture, Implementation,
and Performance",
journal = "IEEE Transaction on Computers",
volume = "C-36",
pages = "1523-1538",
kwds = "prll, warp"
}
@book{ansi:76,
author = "ANSIA",
year = "1978",
title = "American National Standard Programming Language FORTRAN",
publisher = "American National Standards Institute",
address = "New York",
kwds = "book, fortran"
}
-ao- -ap- -aq- -ar-
@article{argg:88,
author = "P. Arbenz and W. Gander and G. H. Golub",
year = "1988",
title = "Restricted Rank Modification of the Symmetric
Eigenvalue Problem: Theoretical Considerations",
journal = "Linear Algebra and Its Applications",
volume = "104",
pages = "75-96",
kwds = "nla, eig, symmetric matrix, updating"
}
@article{argo:88,
author = "P. Arbenz and G. H. Golub",
year = "1988",
title = "On the Spectral Decomposition of {H}ermitian Matrices Subject to
Indefinite Low Rank Perturbations with Applications",
journal = "{SIAM} Journal on Matrix Analysis and Applications",
volume = "9",
pages = "40--58",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, updating, symmetric matrix, indefinite matrix"
}
@article{arbe:91,
author = "P. Arbenz",
year = "1991",
title = "Computing Eigenvalues of Banded Symmetric
Toeplitz Matrices",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "743--754",
kwds = "nla, eig, band matrix, Toeplitz matrix, circulant matrix,
symmetric matrix"
}
@article{argo:92,
author = "P. Arbenz and G. H. Golub",
year = "1992",
title = "QR-Like Algorithms for Symmetric Arrow Matrices",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "655--662",
kwds = "nla, arrowhead matrix, QR algorithm, eig"
}
@article{arro:85,
author = "M. Arioli and F. Romani",
year = "1985",
title = "Relations Between Condition Numbers and the Convergence of the
{J}acobi Method for Real Positive Definite Matrices",
journal = "Numerische Mathematik",
volume = "46",
pages = "31--42",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition, eig, Jacobi's method"
}
@article{arla:86,
author = "M. Arioli and A. Laratta",
year = "1986",
title = "Error Analysis of an Algorithm for Solving an Underdetermined
Linear System",
journal = "Numerische Mathematik",
volume = 46,
pages = "255--268",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, undertermined system"
}
@article{arla:86a,
author = "M. Arioli and A. Laratta",
year = "1986",
title = "Error analysis of algorithms for computing the projection of a
Point onto a linear manifold",
journal = "Linear Algebra Appl.",
volume = 82,
pages = "1--26",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, orthogonalization, projection"
}
@article{ardd:89,
author = "M. Arioli and J. Demmel and I. S. Duff",
year = "1989",
title = "Solving Sparse Linear Systems with Sparse Backward Error",
journal = " SIAM Journal on Matrix Analysis and Applications",
volume = "10",
pages = "165--190",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, pert, backward perturbation"
}
@article{ardr:89,
author = "M. Arioli and I. S. Duff and van Rijk, P. P. M.",
year = "1989",
title = "On the Augmented System Approach to Sparse Least-Squares
Problems",
journal = "Numerische Mathematik",
volume = "55",
pages = "667--685",
kwds = "nla, lsq, pert, sparse"
}
@article{ardn:92,
author = "M. Arioli and I. S. Duff and J. Noailles and D. Ruiz",
year = "1990",
title = "A Block Projection Method for Sparse Matrices",
journal = "SIAM J. Scient. Statist. Comput.",
volume = "13",
pages = "47--70",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, sparse, projection method"
}
@techreport{arca:76,
author = "E. S. Armstrong and A. K. Caglayan",
year = "1976",
title = "An Algorithm for the Weighting Matrices in the Sample-Data Optimal
Linear Regulator Problem",
number = "TN D-8372",
institution = "NASA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, control, weighting"
}
@article{arla:84,
author = "W. F. Arnold and A. J. Laub",
year = "1984",
title = "Generalized Eigenproblem Algorithms and Software for Algebraic
{R}iccati Equations",
journal = "Proceedings of the {IEEE}",
volume = "72",
pages = "1746--1754",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, Riccati equation"
}
@article{arno:51,
author = "W. E. Arnoldi",
year = "1951",
title = "The Principle of Minimized Iterations in the Solution of the
Matrix Eigenvalue Problem",
journal = "Quarterly of Applied Mathematics",
volume = "9",
pages = "17--29",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Arnoldi's method, eig, sparse"
}
@inproceedings{akms:85,
author = "E. Arnould and H. T. Kung and O. Menzileioglu and
K. Sarocky",
year = "1985",
title = "A Systolic Array Computer",
booktitle = "IEEE International Conference on Acoustics, Speach,
and Signal Processing",
editor = "",
pages = "232--235",
publisher = "IEEE",
address = "Washington, DC",
kwds = "cs, warp, systolic"
}
-as-
@phdthesis{ashb:87,
author = "S. F. Ashby",
year = "1987",
title = "Polynomial Preconditioning for Conjugate Gradient Methods",
school = "Computer Science Department, University of Illinois",
address = "ILL",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning"
}
@article{asms:90,
author = "S. F. Ashby and T. A. Manteuffel and P. E. Saylor",
year = "1990",
title = "A Taxonomy for Conjugate Gradient Methods",
journal = "SIAM Journal on Numerical Analysis",
volume = "27",
pages = "1542--1568",
kwds = "nla, conjugate gradients, linear system"
}
@incollection{ashk:71,
author = "V. Ashkenazi",
year = "1971",
title = " Geodetic Normal Equations",
booktitle = "Large Sets of Linear Equations. Ed. J.K. Reid ",
pages = "57--74",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, normal equations, geodesy"
}
@article{aspl:59,
author = "E. Asplund",
year = "1959",
title = "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy
{$a_{ij} = 0$, $j > i+p$}",
journal = "Mathematica Scandinavica",
volume = "7",
pages = "57--60",
note = "Cited in \cite{govl:89}.",
kwds = "la, inverse matrix, band matrix"
}
-at- -au-
@techreport{auch:90,
author = "G. Auchmuty",
year = "1990",
title = "A Posteriori Error Estimates for Linear Equations",
institution = "Department of Mathematics, University of Houston",
type = "Research Report",
number = "UH/MD-91",
kwds = "nla, pert, residual bound, linear system"
}
@article{auto:02,
author = "L. Autonne",
year = "1902",
title = "Sur les groupes lin\'eaires, r\'eels et orthogonaux",
journal = "Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France",
volume = "30",
pages = "121-134",
kwds = "la, polar decomposition"
}
@article{auto:13,
author = "L. Autonne",
year = "1913",
title = "Sur les matrices hypohermitiennes et les unitairs",
journal = "Comptes Rendus de l'Academie des Sciences, Paris",
volume = "156",
pages = "858-860",
kwds = "math, la, svd"
}
@article{auto:15,
author = "L. Autonne",
year = "1915",
title = "Sur les matrices hypohermitiennes et sur les matrices
unitaires",
journal = "Annales De L'Universit\'e de Lyons, Nouvelle S\'erie I",
volume = "38",
pages = "1--77",
kwds = "la, svd, polar decomposition"
}
-av-
@inproceedings{avto:79,
author = "J. K. Avila and J.A. Tomlin",
year = "1979",
title = "Solution of Very Large Least Squares Problems by Nested Dissection
on a Parallel Processor",
booktitle = "In Proceedings of Computer Science and Statistics:
Twelfth Annual Symposium on the Interface",
publisher = "Department of Computer Science",
address = "Waterloo, Canada",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
-aw- -ax-
@incollection{axel:77,
author = "O. Axelsson",
year = "1977",
title = "Solution of Linear Systems of Equations: Iterative Methods",
booktitle = "Sparse Matrix Techniques: {C}openhagen, 1976",
editor = "V. A. Barker",
publisher = "Springer-Verlag",
address = "Berlin",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, iter, sparse"
}
@article{axel:80,
author = "O. Axelsson",
year = "1980",
title = "Conjugate Gradient Type Methods for Unsymmetric and Inconsistent
Systems of Linear Equations",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "1--66",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, conjugate gradients, nonsymmetric matrix"
}
@article{axel:85,
author = "O. Axelsson",
year = "1985",
title = "A Survey of Preconditioned Iterative Methods for Linear Systems of
Equations",
journal = "{BIT}",
volume = "25",
pages = "166--187",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, sparse, iter, preconditioning,
conjugate gradients"
}
@article{axpo:86,
author = "O. Axelsson and B. Polman",
year = "1986",
title = "On Approximate Factorization Methods for Block Matrices Suitable
for Vector and Parallel Processors",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "3--26",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, block matrix, prll"
}
-ay- -az-
-ba-
@incollection{baos:91,
author = "I. Babu\v{s}ka and J. Osborn",
year = "1991",
title = "Eigenvalue Problems",
booktitle = "Handbook of Numerical Analysis, Vol.~II.",
editor = "P. G. Ciarlet and J. L. Lions",
pages = "643--787",
publisher = "Elsevier",
address = "New York",
kwds = "na, eig, functional analysis, pert"
}
@article{bai:88,
author = "Z. Bai",
year = "1988",
title = "Note on the Quadratic Convergence of {Kogbetliantz's}
Algorithm for Computing the Singular Value Decomposition",
journal = "Linear Algebra and Its Applications",
volume = "104",
pages = "131-140",
kwds = "nla, Kogbetliantz's algorithm, svd, Jacobi-like"
}
@unpublished{badm:89,
author = "Z. Bai and J. Demmel and A. Mckenney",
year = "1989",
title = "On the Conditioning of the Nonsymmetric Eigenproblem:
Theory and Software",
note = "LAPACK Working Note",
kwds = "nla, eig, pert, nonsymmetric matrix, condition"
}
@unpublished{bade:92,
author = "Z. Bai and J. W. Demmel",
year = "1991",
title = "On a Direct Algorithm for Computing Invariant Subspaces
with Specified Eigenvalues",
note = "Department of Mathematics, University of Kentucky (first
author). Manuscript submitted to {\it Linear Algebra
and Its Applications.\/}",
kwds = "nla, eig, Schur form"
}
@article{bail:88,
author = "D. Bailey",
year = "1988",
title = "Extra High Speed Matrix Multiplication on the {C}ray-2",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "9",
pages = "603--607",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vect, matrix multiplication"
}
@article{bana:22,
author = "S. Banach",
year = "1922",
title = "Sur les op\'erations dans les ensembles abstraits
et leur application aux \'equations integrales",
journal = "Fundamenta Mathematicae",
volume = "3",
pages = "133--181",
kwds = "norm, Banach space, functional analysis"
}
@article{bana:29,
author = "S. Banach",
year = "1929",
title = "Sur les functionnelles lin\'eaires {II}.",
journal = "Studia Mathematica",
volume = "1",
pages = "223-239",
kwds = "Hahn-Banach theorem, functional analysis"
}
@book{bana:32,
author = "S. Banach",
year = "1932",
title = " {Th\'eorie Op\'erations Lin\'eaires}",
publisher = "Hafner Publishing Co.",
address = "New York",
kwds = "book, Banach space, Hahn-Banach theorem, functional analysis"
}
@article{baro:77,
author = "R. E. Bank",
year = "1977",
title = "Marching Algorithms for Elliptic Boundary Value Problems.
{I}: The Constant Coefficient Case",
journal = "SIAM Journal on Numerical Analysis",
volume = "14",
pages = "950-970",
kwds = "pde, elliptic pde"
}
@article{bank:77,
author = "R. E. Bank",
year = "1977",
title = "Marching Algorithms for Elliptic Boundary Value Problems.
{II}: The Variable Coefficient Case",
journal = "SIAM Journal on Numerical Analysis",
volume = "14",
pages = "950-970",
kwds = "pde, elliptic pde"
}
@book{bard:74,
author = "Y. Bard",
year = "1974",
title = "Nonlinear Parameter Estimation",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, stat, nlop, lsq, nllsq"
}
@techreport{bare:82,
author = "E. H. Bareiss",
year = "1982",
title = "Numerical Solution of the Weighted Linear Least Squares Problems
by {G}-transformations",
institution = "Department of Electrical Engineering and Computer Science",
adress = "Northwestern University, Evanston, Illinois",
type = "Technical Report",
number = "82-03-NAM-03, April 1982",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, weights"
}
@techreport{bamv:47,
author = "V. Bargmann and D. Mongomery and von Neumann, J.",
year = "1947",
title = "Solutions of Linear Systems of High Order",
institution = "Navy Bu. Ord.",
type = "Report",
number = "",
note = "In \cite[V.~4, 421--478]{vneu:62}.",
kwds = "nla, rounding error, linear system"
}
@article{bari:75,
author = "I. Y. Bar-Itzhack",
year = "1975",
title = "Iterative Optimal Orthogonalization of the Strapdown Matrix",
journal = "{IEEE} Transactions on Aerospace and Electronic Systems",
volume = "11",
pages = "30--37",
note = "Cited in \cite{govl:89}.",
kwds = "nla, iter, orthogonalization"
}
@unpublished{bapl:,
author = "G. P. Barker and R. J. Plemmons",
year = "1984?",
title = "Convergence of {Gauss-Seidel} Iterations for Computing
Stationary Distributions of {Markov} Chains",
note = "Manuscript, North Carolina State University",
kwds = "nla, Markov chain, Gauss-Seidel iteration, iter, relaxation"
}
@article{barl:85,
author = "J. L. Barlow",
year = "1985",
title = "Stability Analysis of the {G}-algorithm and a
Note on its Application to Sparse Least Squares Problems",
journal = "BIT",
volume = "25",
pages = "507--520",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, weights, sparse"
}
@article{baba:85,
author = "J. L. Barlow and E. H. Bareiss",
year = "1985",
title = "On Roundoff Error Distributions in Floating Point
and Logarithmic Arithmetic",
journal = "Computing",
volume = "24",
pages = "325--347",
kwds = "rounding error, stochastic analysis, computer arithmetic"
}
@article{baba:85a,
author = "J. L. Barlow and E. H. Bareiss",
year = "1985",
title = "Probabilistic Error Analysis of Gaussian Elimination
in Floating Point and Logarithmic Arithmetic",
journal = "Computing",
volume = "34",
pages = "349--364",
kwds = "nla, lud, rounding error, stochastic analysis, computer arithmetic"
}
@article{barl:86,
author = "J. L. Barlow",
year = "1986",
title = "On the Smallest Positive Singular Value of a Singular
{$M$}-Matrix with Applications to Ergodic {Markov} Chains",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "7",
pages = "414--424",
kwds = "nla, Markov chain, M-matrix, svd, singular system"
}
@article{baip:87,
author = "J. L. Barlow and I. C. F. Ipsen",
year = "1987",
title = "Scaled {Givens} Rotations for the Solution of Linear
Least Squares Problems on Systolic Arrays",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "716-734",
kwds = "nla, prll, qrd, lsq, systolic, plane rotation"
}
@article{barl:88,
author = "J. L. Barlow",
year = "1988",
title = "Error Analysis and Implementation Aspects of Deferred Correction
for Equality Constrained Least Squares Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "25",
pages = "1340--1358",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, rounding error, constraints"
}
@techreport{bade:88,
author = "J. Barlow and J. Demmel",
year = "1988",
title = "Computing Accurate Eigensystems of Scaled Diagonally
Dominant Matrices",
institution = "Computer Science Department, Courant Institute",
type = "Technical Report",
number = "421",
note = "Cited in \cite{deve:89}. To appear in {\it SIAM Journal
on Numerical Analysis\/}",
kwds = "la, nla, pert, eig, diagonal dominance"
}
@article{baha:88,
author = "J. L. Barlow and S. L. Handy",
year = "1988",
title = "The Direct Solution of Weighted and Equality
Constrained Least-Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "704-716",
kwds = "nla, lsq, constraints, weights"
}
@article{banp:88,
author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
year = "1988",
title = " Iterative Methods for Equality-constrained Least Squares
Problems.",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "892--906",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, iter, constraints"
}
@techreport{barl:90,
author = "J. L. Barlow",
year = "1990",
title = "Error Analysis of a Pairwise Summation Algorithm
to Compute the Sample Variance",
institution = "Department of Computer Science, Pennsylvania State
University",
type = "Technical Report",
number = "CS-90-10",
kwds = "stat, variance, standard deviation"
}
@techreport{barl:91,
author = "J. L. Barlow",
year = "1991",
title = "Error Analysis of Update Methods for the Symmetric
Eigenvalue Problem",
institution = "Department of Computer Science, Pennsylvania
State University",
type = "Technical Report",
number = "CS-91-09",
kwds = "nla, prll, eig, symmetric matrix, update"
}
@techreport{barl:91a,
author = "J. L. Barlow",
year = "1991",
title = "Error Bounds and Condition Estimates for the Computation
of Null Vectors with Applications to {Markov} Chains",
institution = "Department of Computer Science, Pennsylvania
State University",
type = "Technical Report",
number = "CS-91-20",
kwds = "la, nla, eig, condition estimation, Markov chain"
}
@techreport{bave:91,
author = "J. L. Barlow and U. B. Vemulapati",
year = "1991",
title = "Rank Detection Methods for Sparse Matrices",
institution = "Department of Computer Science, Pennsylvania
State University",
type = "Technical Report",
number = "CS-91-21",
kwds = "nla, condition estimation, rank determination"
}
@article{bast:68,
author = "S. Barnett and C. Storey",
year = "1968",
title = "Some Applications of the {L}yapunov Matrix Equation",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "4",
pages = "33--42",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lyapunov equation, matrix equation"
}
@techreport{barr:88,
author = "Anders Barrlund",
year = "1988",
title = "Perturbation Bounds on the Polar Decomposition",
institution = "Institute of Information Processing, University
of Ume{\aa}",
type = "Report",
number = "UMINF-146.88",
kwds = "la, pert, polar decomposition"
}
@article{barr:91,
author = "A. Barrland",
year = "1991",
title = "Perturbation Bounds for the {$LDL^{\rm H}$} and
the {$LU$}~factorizations",
journal = "BIT",
volume = "31",
pages = "358--363",
kwds = "la, pert, lud"
}
@article{baro:73,
author = "I. Barrodale and F. D. K. Roberts",
year = "1973",
title = "An Improved Algorithm for Discrete $\ell_1$ Linear Approximation",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "839--848",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, l1 approximation"
}
@article{baph:75,
author = "I. Barrodale and C. Phillips",
year = "1975",
title = "Algorithm 495: Solution of an Overdetermined System of
Linear Equations in the Chebychev Norm ",
journal = "ACM Transactions on Mathematical Software",
volume = "1",
pages = "264--270",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Chebyshev approximation"
}
@article{bast:77,
author = "I. Barrodale and G. F. Stuart",
year = "1977",
title = "A New Variant of {Gaussian} Elimination",
journal = "Journal Inst.\ Maths.\ Applics.",
volume = "19",
pages = "39-47",
kwds = "nla, lud"
}
@article{baro:78,
author = "I. Barrodale and F. D. K. Roberts",
year = "1978",
title = "An Efficient Algorithm for Discrete $\ell_1$ Linear Approximation
with Linear Constraints",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "603--611",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, l1 approximation"
}
@article{bgkv:80,
author = "H. Bart and I. Gohberg and M. A. Kaashoek and Van Dooren, P.",
year = "1980",
title = "Factorization of Transfer Functions",
journal = "SIAM Journal on Control and Optimization",
volume = "18",
pages = "675--696",
kwds = "la, transfer function"
}
@article{bago:69,
author = "R. H. Bartels and G. H. Golub",
year = "1969",
title = "The Simplex Method of Linear Programming Using {LU}~Decomposition",
journal = "Communications of the ACM",
volume = "12",
pages = "266-268",
kwds = "nla, nlop, lud, linear programming, updating"
}
@incollection{bags:70,
author = "R. H. Bartels and G. H. Golub and M. A. Saunders",
year = "1970",
title = "Numerical Techniques in Mathematical Programming",
pages = "123--176",
booktitle = "Nonlinear programming",
editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter",
publisher = "Academic Press, New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, rank determination"
}
@article{bart:71,
author = "R. H. Bartels",
year = "1971",
title = "A Stablization of the Simplex Method",
journal = "Numerische Mathematik",
volume = "16",
pages = "414--434",
kwds = "nlop, simplex method, updating"
}
@incollection{basz:71,
author = "R. H. Bartels and J. Stoer and C. Zenger",
year = "1971",
title = "A Realization of the Simplex Method Based on
Triangular Decomposition",
booktitle = "Linear Algebra",
editor = "J. H. Wilkinson and C. Reinsch",
pages = "152--190",
publisher = "Springer",
address = "New York",
kwds = "nla, linear programming, simplex method, lud, updating"
}
@article{bast:72,
author = "R. H. Bartels and G. W. Stewart",
year = " 1972",
title = "Algorithm 432: The Solution of the Matrix
Equation {$AX - BX = C$}",
journal = "Communications of the ACM",
volume = "8",
pages = "820-826",
kwds = "nla, Schur form, Sylvester equation, Lyapunov equation,
matrix equation"
}
@article{bacs:78,
author = "R. H. Bartels and A. R. Conn and J. W. Sinclair",
year = "1978",
title = "Minimization Techniques for Piecewise Differentiable Functions:
The {$L_{1}$} Solution to an Overdetermined Linear System",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "15",
pages = "224--241",
note = "Cited in \cite{govl:89}.",
kwds = "nla, l1 approximation, overdetermined system"
}
@article{bacc:78,
author = "R. H. Bartels and A. R. Conn and C. Charalambous",
year = "1978",
title = "On {C}line's Direct Method for Solving Overdetermined
Linear Systems in the {$L_{\infty}$} Sense",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "15",
pages = "255--270",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Chebyshev approximation, overdetermined system"
}
@article{baco:80,
author = "R. H. Bartels and A. R. Conn",
year = "1980",
title = "Linearly Constrained Discrete $\ell_1$ Problems",
journal = "ACM Transactions on Mathematical Software",
volume = "6",
pages = "594--608",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, l1 approximation, software"
}
@article{bacc:80,
author = "R. H. Bartels and A. R. Conn and C. Charalambous",
year = "1980",
title = "On {Cline's} Direct Method for Solving Overdetermined
Linear Systems in the {$\ell_\infty$} Sense",
journal = " SIAM Journal on Numerical Analysis",
volume = "15",
pages = "255--270",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, Chebyshev approximation"
}
@article{bacs:78,
author = "R. H. Bartels and A. R. Conn and J. W. Sinclair",
year = "1978",
title = "Minimization Techniques for Piecewise Differentiable Functions:
The $\ell_1$ Solution to an Overdetermined Linear System",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "224--241",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, l1 approximation"
}
@article{bamw:67,
author = "W. Barth, R. S. Martin and J. H. Wilkinson",
year = "1967",
title = "Calculation of the Eigenvalues of a Symmetric
Tridiagonal matrix by the Method of Bisection",
journal = "Numerische Mathematik",
volume = "9",
pages = "386--393",
note = "Also in \cite[pp.249--256]{wire:71}.",
kwds = "nla, eig, symmetric matrix, tridiagonal matrix, software"
}
@article{bart:54,
author = "Helmut Bartsch",
year = "1954",
title = " {Absch\"atzungen f\"ur die kleinste charakteristische
Zahl einer positiv-definiten hermiteschen Matrix}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Mechanik}",
volume = "34",
pages = "72-74",
kwds = "la, pert, eig, symmetric matrix"
}
@article{bage:76,
author = "V. Barwell and J. A. George",
year = "1976",
title = "A Comparison of Algorithms for Solving Symmetric Indefinite
Systems of Linear Equations",
journal = "{ACM} Transactions on Mathematical Software",
volume = "2",
pages = "242--251",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, symmetric matrix, indefinite system"
}
@article{bate:08,
author = "H. Bateman",
year = "1908",
title = "A Formula for the Solving Function of a Certain
Integral Equation of the Second Kind",
journal = "Transactions of the Cambridge Philosophical Society",
volume = "20",
pages = "179-187",
kwds = "na, la, svd, integral equation"
}
@article{bate:08a,
author = "H. Bateman",
year = "1908",
title = "The Reality of the Roots of Certain Transcendental
Equations Occurring in the Theory of Integral
Equations",
journal = "Transactions of the Cambridge Philosophical Society",
volume = "20",
pages = "371--381",
kwds = "na, la, svd, integral equation"
}
@article{bate:08b,
author = "H. Bateman",
year = "1908",
title = "On the Application of Integral Equations to the Determination
of Upper and Lower Limits of a Double Integral",
journal = "Transactions of the Cambridge Philosophical Society",
volume = "21",
pages = "123--128",
kwds = "na, la, svd, integral equation"
}
@article{bate:22,
author = "H. Bateman",
year = "1922",
title = "On the Numerical Solution of Linear Integral Equations",
journal = "Proceedings of the Royal Society of London, Series A",
volume = "100",
pages = "441--449",
kwds = "na, la, svd, integral equation"
}
@techreport{bawo:82,
author = "D. M Bates and D. A. Wolf",
year = "1982",
title = "Non-negative Regression by Givens Rotations",
institution = "Department of Statistics,
University of Wisconsin",
number = "687",
kwds = "stat, nla, regr, plane rotation"
}
@article{bawi:72,
author = "K.-J. Bathe and E. L. Wilson",
year = "1972",
title = "Large Eigenvalue Problems in Dynamic Analysis",
journal = "ASCE J., Eng. Mech. Div.",
volume = "98",
pages = "1471--1485",
kwds = "nla, eig, sparse"
}
@article{bawi:73,
author = "K.-J. Bathe and E. L. Wilson",
year = "1973",
title = "Solution Methods for Eigenvalue Problems in
Structural Mechanics",
journal = "International Journal for Numerical Methods in Engineering",
volume = "6",
pages = "213-266",
kwds = "nla, eig, sparse"
}
@article{bawi:73a,
author = "K.-J. Bathe and E. L. Wilson",
year = "1973",
title = "Eigensolution of Large Structural Systems with
Small Bandwidth",
journal = "ASCE J., Eng. Mech. Div.",
volume = "99",
pages = "467--480",
kwds = "nla, eig, sparse"
}
@article{baue:54,
author = "F. L. Bauer",
year = "1954",
title = " {Beitr\"age zur Entwicklung numerischer Verfahren
f\"ur programmgesteuerte Rechenanlagen I. Quadratisch
konvergente Durchf\"uhrung der Bernoulli-Jacobischen
Methode zur Nullstellenbestimmung von Polynomen}",
journal = "Bayer.\ Akad.\ Wiss.\ Math.-Natur.\ Kl.\ S.-B.",
pages = "275--303",
kwds = "nlop, polynomial, Bernoulli's method"
}
@article{baue:56,
author = "F. L. Bauer",
year = "1956",
title = " {Beitr\"age zur Entwicklung numerischer Verfahren
f\"ur programmgesteuerte Rechenanlagen II. Direkte
Faktorisierung eines Polynoms}",
journal = "Bayer.\ Akad.\ Wiss.\ Math.-Natur.\ Kl.\ S.-B.",
pages = "163--203",
kwds = "nlop, polynomial"
}
@article{baue:56a,
author = "F. L. Bauer",
year = "1956",
title = " {Das Verfahren der abgek\"urzten Iteration f\"ur algebraische
Eigenwertprobleme, insbesondere zur Nullstellenbestimmung
eines Polynoms}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "7",
pages = "17-32",
kwds = "nla, nlop, polynomial, eig"
}
@article{baue:57,
author = "F. L. Bauer",
year = "1957",
title = "{Das Verfahren der Treppeniteration und verwandte
Verfahren zur L\"osung algebraischer Eigenwertprobleme}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "8",
pages = "214--235",
kwds = "nla, eig, subspace iteration, Treppeniteration, sparse"
}
@article{basa:57,
author = "F. L. Bauer and Klaus Samelson",
year = "1957",
title = "Polynomkerne und Iterationsverfahren",
journal = "Math.\ Z.",
volume = "67",
pages = "93-98",
kwds = "nla, linear system, iter"
}
@article{baue:58,
author = "F. L. Bauer",
year = "1958",
title = "On Modern Matrix Iteration Processes of {Bernoulli}
and {Graeffe} Type",
journal = "Journal of the ACM",
volume = "5",
pages = "246-257",
kwds = "nla, nlop, polynomial, Bernoulli's method, Graeffe's method"
}
@article{baue:59,
author = "F. L. Bauer",
year = "1959",
title = "Sequential Reduction to Tridiagonal Form",
journal = "SIAM Journal",
volume = "7",
pages = "107--113",
kwds = "nla, eig, tridiagonal matrix"
}
@article{bafi:60,
author = "F. L. Bauer and C. T. Fike",
year = "1960",
title = "Norms and Exclusion Theorems",
journal = "Numerische Mathematik",
volume = "2",
pages = "137--141",
kwds = "la, eig, norm, pert"
}
@article{baho:60,
author = "F. L. Bauer and A. S. Householder",
year = "1960",
title = "Moments and Characteristic Roots",
journal = "Numerische Mathematik",
volume = "2",
pages = "42--43",
kwds = "la, eig, pert"
}
@article{baue:62,
author = "F. L. Bauer",
year = "1962",
title = "On the Field of Values Subordinate to a Norm",
journal = "Numerische Mathematik",
volume = "4",
pages = "103-113",
kwds = "la, field of values, norm"
}
@article{baue:63,
author = "F. L. Bauer",
year = "1963",
title = "Optimally Scaled Matrices",
journal = "Numerische Mathematik",
volume = "5",
pages = "73--87",
kwds = "nla, scaling"
}
@article{baue:65,
author = "F. L. Bauer",
year = "1965",
title = "Elimination with Weighted Row Combinations for Solving
Linear Equations and Least Squares Problems",
journal = "Numerische Mathematik",
volume = "7",
pages = "338-352",
note = "Also in \cite[pp.119--133]{wire:71}.",
kwds = "nla, lsq, Gram-Schmidt algorithm, software"
}
@article{baue:66,
author = "F. L. Bauer",
year = "1966",
title = " {Genauigkeitsfragen bei der L\"osung linear
Gleich\-ungs\-systeme}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Mechanik}",
volume = "46",
pages = "409--421",
kwds = "la, pert, condition, scaling"
}
@article{baue:66a,
author = "F. L. Bauer",
year = "1966",
title = "Inclusion Sets for Roots of Polynomials",
journal = "Numerische Mathematik",
volume = "9",
pages = "173-176",
kwds = "nlop, pert, polynomial"
}
@techreport{baue:67,
author = "F. L. Bauer",
year = "1967",
title = "Theory of Norms",
institution = "Computer Science Department School of Humanities and
Sciences, Stanford University",
type = "Technical Report",
number = "CS 75",
kwds = "la, norm"
}
@article{bare:68,
author = "F. L. Bauer and C. Reinsch",
year = "1968",
title = "Rational {QR} Transformation with {N}ewton Shift for Symmetric
Tridiagonal Matrices",
journal = "Numerische Mathematik",
volume = "11",
pages = "264--272",
note = "Also in \cite[pages 257--265]{WilR71}",
note = "Cited in \cite{govl:89}.",
kwds = "nla, QR algorithm, tridiagonal matrix"
}
@article{bads:69,
author = "F. L. Bauer and E. Deutsch and J. Stoer",
year = "1969",
title = " {Absch\"atzungen F\"ur die Eigenwerte positiver linearer
Operatoren}",
journal = "Linear Algebra and Its Applications",
volume = "2",
pages = "275-301",
kwds = "la, pert, eig"
}
@incollection{bare:70,
author = "F. L. Bauer and C. Reinsch",
year = "1970",
title = "Inversion of Positive Definite Matrices by the {G}auss-{J}ordan
Methods",
booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra",
editor = "J. H. Wilkinson and C. Reinsch",
publisher = "Springer-Verlag",
address = "New York",
pages = "45--49",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, Gauss-Jordan method"
}
@book{baum:72,
author = "H. Baumg{\"a}rtel",
year = "1972",
title = " {Endlich\-dimensionale Analytische St\"orungs\-theorie}",
publisher = "Akademie-Verlag",
address = "Berlin",
note = "Cited in \cite{bhat:87}.",
kwds = "book, la, pert, eig"
}
@article{bast:79,
author = "C. Bavely and G. W. Stewart",
year = "1979",
title = "An Algorithm for Computing Reducing Subspaces
by Block Diagonalization",
journal = "SIAM Journal on Numerical Analysis",
volume = "16",
pages = "359-367",
kwds = "nla, eig, invariant subspace, nonsymmetric matrix"
}
@article{bawi:70,
author = "R. Bayer and C. Witzgall",
year = "1970",
title = "Some Complete Calculi for Matrices",
journal = "Communications of the ACM",
volume = "13",
pages = "223--237",
kwds = "la, cs"
}
-bb- -bc- -bd- -be-
@techreport{beat:64,
author = "A. E. Beaton",
year = "1964",
title = "The use of Special Matrix Operators in Statistical Calculus",
institution = "Educational Testing Service,
Princeton, New Jersey",
type = "Research Bulletin",
number = "64-51",
kwds = "stat, nla, sweep operator, updating, inverse matrix"
}
@article{berb:76,
author = "A. E. Beaton and D. B. Rubin and J. L. Barone",
year = "1976",
title = "The Acceptability of Regression Solutions: Another Look at
Computational Accuracy",
journal = "Journal of the American Statistical Association",
volume = "71",
pages = "158-168",
kwds = "stat, regr, pert, eriv, rounding error, diagnostic"
}
@article{beco:83,
author = "R. J. Bechman and R. D. Cook",
year = "1983",
title = "Outlier..........s",
journal = "Technometrics",
volume = "25",
pages = "119-149",
kwds = "stat, regr, diagnostic, outlier"
}
@book{bebe:71,
author = "E. F. Beckenbach and R. Bellman",
year = "1971",
title = "Inequalities",
publisher = "Springer",
address = "New York",
kwds = "book, na, la, inequalities, pert"
}
@article{bevd:88,
author = "Th. Beelen and Van Dooren, P.",
year = "1988",
title = "An Improved Algorithm for the Computation of {Kronecker's}
Canonical Form of a Singular Pencil",
journal = "Linear Algebra and Its Applications",
volume = "105",
pages = "9-66",
kwds = "la, nla, eig, geig, matrix pencil, Kronecker form"
}
@techreport{bdgm:91,
author = "A. Beguelin and J. J. Dongarra and A. Geist and
R. Mancheck and V. Sunderam",
year = "1991",
title = "A Users' Guide to PVM (Parallel Virtual Machine)",
institution = "Oak Ridge National Laboratory",
type = "Technical Report",
number = "ORNL/TM-11826",
kwds = "prll, operating system"
}
@book{bell:70,
author = "R. Bellman",
year = "1970",
title = "Introduction to Matrix Analysis",
publisher = "Mc Graw-Hill",
address = "New York",
kwds = "book, la"
}
@book{bekw:80,
author = "D. A. Belsley and A. E. Kuh and R. E. Welsch",
year = "1980",
title = "Regression Diagnostics: Identifying Influential Data and Sources
of Collinearity",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, stat, regr, diagnostic, eriv, outlier, collinearity"
}
@article{bels:82,
author = "D. A. Belsley",
year = "1982",
title = "Assessing the Presence of Harmful Collinearity and Other
Forms of Weak Data Through a Test for Signal-to-Noise",
journal = "Journal of Econometrics",
volume = "20",
pages = "211--253",
kwds = "stat, regr, eriv, collinearity, diagnostic"
}
@article{bels:84,
author = "D. A. Belsley",
year = "1984",
title = "Demeaning Conditioning Diagnostics Through Centering",
journal = "The American Statistician",
volume = "38",
pages = "73-77",
kwds = "stat, regr, diagnostic, eriv, centering"
}
@article{belt:1873,
author = "E. Beltrami",
year = "1873",
title = "Sulle Funzioni Bilineari",
journal = "Giornale di Matematiche ad Uso degli Studenti Delle Universita",
volume = "11",
pages = "98-106",
note = "An English translation by D. Boley is available as University
of Minnesota, Department of Computer Science, Technical
Report 90--37, 1990.",
kwds = "la, svd, history"
}
@article{besk:70,
author = "C. F. Bender and I. Shavitt",
year = "1970",
title = "An Iterative Procedure for the Calculation of the Lowest
Real Eigenvalue and Eigenvector of a Nonsymmetric Matrix",
journal = "J. Comput. Phys.",
volume = "6",
pages = "146--149",
kwds = "nla, eig, sparse, nonsymmetric matrix"
}
@article{bend:02,
author = "I. Bendixson",
year = "1902",
title = "Sur les racines d'une equation fondemental",
journal = "Acta Mathematica",
volume = "3",
pages = "359-366",
kwds = "la, Bendixson's theorem"
}
@article{beni:66,
author = "A. Ben-Israel",
year = "1966",
title = "On Error Bounds for Generalized Inverses",
journal = "SIAM Journal on Numerical Analysis",
volume = "3",
pages = "585--592",
kwds = "la, pert, ginv"
}
@book{begr:73,
author = "A. Ben-Israel and T. N. E. Greville",
year = "1973",
title = "Generalized Inverses: Theory and Applications",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, la, ginv"
}
@article{bebc:88,
author = "M. Bennani and M. C. Brunet and F. Chatelin",
year = "1988",
title = "De l'utilisation en calcul matriciel de mod\`eles
probabilistes pour la simulation des erreurs de calcul",
journal = "Comptes Rendus de l'Acad\'emie des Sciences Paris, S\'erie I",
volume = "307",
pages = "847--850",
kwds = "nla, pert, rounding error, stochastic analysis"
}
@article{beno:24,
author = "Commandant Beno{\^\i}t",
year = "1924",
title = "Note sur une m\'ethode de r\'esolution des \'equations
normales provenant de l'application de la m\'ethode des
moindres c\'arres a un syst\`em d'\'equations lin\'eares
en nombre inf\'erieur \`a celui des inconnues. --- Application
de la m\'ethode \`a la r\'esolution d'un syst\`eme
d\'eini d'\'equations lin\'eares ({Proc\'ed\'e du
Commandant Cholesky})",
journal = "Bull\'etin G\'eod\'esique (Toulouse)",
volume = "2",
pages = "5--77",
kwds = "nla, Cholesky decomposition, lud"
}
@techreport{begr:66,
author = "J. M. Bennett and D. R. Green",
year = "1966",
title = "Updating the Inverse or Triangular Factors of a Modified
Matrix",
institution = "Computing Department, Univerisity of Sidney",
number = "42",
kwds = "nla, updating, inverse matrix, lud"
}
@article{bpsz:50,
author = "P. G. Bergman and R. Penfield and R. Schiller and H. Zatkis",
year = "1950",
title = "The {Hamiltonian} of the General Theory of Relativity
with Electromagnetic Field",
journal = "Physical Review",
volume = "52",
pages = "1950",
kwds = "la, ginv"
}
@inproceedings{berk:76,
author = "K. N. Berk",
year = "1976",
title = "Tolerance and Condition in Regression Computations",
booktitle = "In Proceedings of the Ninth
Interface Symposium on Computer
Science and Statistics",
publisher = "Prindle, Weber, and Schmidt",
address = "Boston",
kwds = "stat, regr, condition, rank determination"
}
@article{berk:77,
author = "K. N. Berk",
year = "1977",
title = "Tolerance and Condition in Regression Computations",
journal = "Journal of the American Statistical Association",
volume = "72",
pages = "863--866",
kwds = "stat, regr, condition, rank determination"
}
@article{berk:78,
author = "K. N. Berk",
year = "1978",
title = "Comparing Subset Regression Procedures",
journal = "Technometrics",
volume = "20",
pages = "1--6",
kwds = "stat, regr, variable selection"
}
@article{berk:63,
author = "E. Berkson",
year = "1963",
title = "Some Metrics on the Subspaces of a Banach Space",
journal = "Pacific Journal of Mathematics",
volume = "13",
pages = "7--22",
kwds = "la, subspace metric, functional analysis"
}
@article{berk:50,
author = "J. Berkson",
year = "1950",
title = "Are There Two Regressions",
journal = "Journal of the American Statistical Association",
volume = "45",
pages = "164-180",
kwds = "stat, regr, eriv"
}
@article{bebe:71,
author = "A. Berman and A. Ben-Israel",
year = "1971",
title = "A Note on Pencils of {H}ermitian of Symmetric Matrices",
journal = "{SIAM} Journal on Applied Mathematics",
volume = "21",
pages = "51--54",
note = "Cited in \cite{govl:89}.",
kwds = "la, geig, symmetric matrix"
}
@article{beve:68,
author = "M. J. M. Bernal and J. H. Verner",
year = "1968",
title = "On Generalizations of the Theory of Consistent Orderings for
Successive Over-Relaxation Methods",
journal = "Numerische Mathematik",
volume = "12",
pages = "215--222",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, relaxation, iter"
}
@inproceedings{besa:86,
author = "M. Berry and A. Sameh",
year = "1986",
title = "Multiprocessor {J}acobi Algorithms for Dense Symmetric Eigenvalue
and Singular Value Decompositions",
booktitle = "Proceedings International Conference on Parallel Processing",
pages = "433--440",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, Jacobi-like, eig, svd"
}
@article{bego:91,
author = "M. Berry and G. H. Golub",
year = "1991",
title = "Estimating the Largest Singular Values of Large Sparse
Matrices via Modified Moments",
journal = "Numerical Algorithms",
volume = "1",
pages = "363--374",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, svd"
}
@article{bert:1855,
author = "J. Bertrand",
year = "1855",
title = "Sur la m\'ethode des moindres carr\'es",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "40",
pages = "1190--1192",
kwds = "la, Gauss, lsq, history"
}
@article{becr:88,
author = "R. Bevilacqua and B. Codenotti and F. Romani",
year = "1988",
title = "Parallel Solution of Block Tridiagonal Linear Systems",
journal = "Linear Algebra and Its Applications",
volume = "104",
pages = "39-58",
kwds = "nla, prll, tridiagonal matrix"
}
-bf- -bg- -bh-
@article{bhdm:83,
author = "R. Bhatia and C. Davis and A. McIntosh",
year = "1983",
title = "Perturbation of Spectral Subspaces and Solution of Linear
Operator Equations",
journal = "Linear Algebra and Its Applications",
volume = "52-53",
pages = "45--67",
kwds = "la, pert, eig, invariant subspace, normal matrix"
}
@article{bhda:84,
author = "R. Bhatia and C. Davis",
year = "1984",
title = "A Bound for the Spectral Variation of a Unitary Operator",
journal = "Linear and Multilinear Algebra",
volume = "15",
pages = "71--76",
kwds = "la, pert, eig, orthogonal matrix"
}
@article{bhho:85,
author = "R. Bhatia and J. A. R. Holbrook",
year = "1985",
title = "Short Normal Paths and Spectral Variation",
journal = "Proceedings of the American Mathematical Society",
volume = "94",
pages = "377--382",
kwds = "la, pert, eig, orthogonal matrix, normal matrix"
}
@book{bhat:87,
author = "R. Bhatia",
year = "1987",
title = "Perturbation Bounds for Matrix Eigenvalues",
series = "Pitman Research Notes in Mathematics",
publisher = "Longmann Scientific \& Technical",
address = "Harlow, Essex",
note = "Published in the USA by John Wiley.",
kwds = "book, la, pert, eig"
}
@unpublished{bhdk:87,
author = "R. Bhatia and C. Davis and P. Koosis",
year = "1987",
title = "An Extremal Problem in {Fourier} Analysis with Applications
to Operator Theory",
note = "Preprint cited in \cite{bhat:87}",
kwds = "la, functional analysis, invariant subspace"
}
@article{bhdk:91,
author = "R. Bhatia and C. Davis and F. Kittaneh",
year = "1991",
title = "Some Inequalities for Commutators and an Application
to Spectral Variation",
journal = "Aequationes Mathematicae",
volume = "41",
pages = "70--78",
kwds = "la, eig, pert, symmetric matrix, orthogonal matrix"
}
@unpublished{bhbh:91,
author = "R. Bhatia and T. Bhattacharyya",
year = "1991",
title = "A {Henrici} Theorem for Joint Spectra of Commuting Matrices",
note = "Manuscript, Indian Statistical Institute.",
kwds = "la, eig, pert, Clifford algebra, commuting matrices"
}
@unpublished{bhbh:91a,
author = "R. Bhatia and T. Bhattacharyya",
year = "1991",
title = "A Generalization of the {Hoffman--Wielandt} Theorem",
note = "Manuscript, Indian Statistical Institute.",
kwds = "la, eig, pert, Clifford algebra, commuting matrices"
}
@unpublished{bhat:92,
author = "R. Bhatia",
year = "1992",
title = "On Residual Bounds for Eigenvalues",
note = "Manuscript, Indian Statistical Institute.",
kwds = "la, eig, pert, residual bound"
}
-bi-
@article{bipa:88,
author = "D. Bini and V. Pan",
year = "1988",
title = "Efficient Algorithms for the Evaluation of the Eigenvalues
of (Block) Banded {Toeplitz} Matrices",
journal = "Mathematics of Computation",
volume = "50",
pages = "431-448",
kwds = "nla, prll, Toeplitz matrix, fast algorithm"
}
@article{birk:46,
author = "G. D. Birkhoff",
year = "1946",
title = "Tres Observaciones Sobre el Algebra Lineal",
journal = "Universidad Nacional de Tucuman Revista, Serie A",
volume = "5",
pages = "147--151",
annote = "{The citation to K\"onig is the same as in Hall.}",
kwds = "la, convexity, doubly stochastic matrix"
}
@incollection{bivl:86,
author = "C. H. Bischof and Van Loan, C.",
year = "1986",
title = "Computing the {SVD} on a Ring of Array Processors",
booktitle = "Large Scale Eigenvalue Problems",
editor = "J. Cullum and R. Willoughby",
publisher = "North-Holland",
pages = "51--66",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, prll"
}
@incollection{bisc:87,
author = "C. H. Bischof",
year = "1987",
title = "The Two-Sided Block {J}acobi Method on Hypercube Architectures",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = "{SIAM} Publications",
address = "Philadelphia",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Jacobi's method, block algorithm, prll, hypercube"
}
@article{bivl:87,
author = "C. H. Bischof and C. Van Loan",
year = "1987",
title = "The {$WY$} Representation for Products of
{Householder} Transformations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "s2-s13",
kwds = "nla, prll, Householder transformation, qrd,
memory hierarchy"
}
@techreport{bisc:88,
author = "C. H. Bischof",
year = "1988",
title = "Computing the Singular Value Decomposition on a
Distributed System of Vector Processors",
number = "87 869",
institution = "Computer Science Department, Cornell University",
address = "Ithaca, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, prll"
}
@phdthesis{bisc:88a,
author = "C. H. Bischof",
year = "1988",
title = "{QR} Factorization Algorithms for Coarse Grain
Distributed Systems",
school = "Computer Science, Cornell University",
address = "Ithaca, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, prll"
}
@inproceedings{bisc:89,
author = "C. H. Bischof",
year = "1989",
title = "A Block {QR}~Factorization Algorithm Using Restructed
Pivoting",
booktitle = "SUPERCOMPUTING '89",
pages = "248--256",
publisher = "ACM Press",
address = "New York",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, qrd, block algorithm, rank determination"
}
@techreport{biha:89,
author = "C. H. Bischof and P. C. Hansen",
year = "1989",
title = "Structure-Preserving and Rank-Revealing {QR}-Factorizations",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Preprint",
number = "MCS-P100-0989",
kwds = "nla, condition estimation"
}
@techreport{bilp:89,
author = "C. H. Bischof and J. G. Lewis and D. J. Pierce",
year = "1989",
title = "Incremental Condition Estimation for General Matrices",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Preprint",
number = "MCS-P106-0989",
kwds = "nla, condition estimation"
}
@article{bisc:90,
author = "C. H. Bischof",
year = "1990",
title = "Incremental Condition Estimation",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "312--322",
kwds = "nla, condition estimation"
}
@techreport{bisc:90a,
author = "C. H. Bischof",
year = "1990",
title = "Adaptive Condition Estimation for Rank-one Updates of {QR}
Factorizations",
institution = "Argonne National Laboratory, Mathematics
and Computer Sciences Division",
type = "Technical Report",
number = "ANL/MCS-P166-0790",
kwds = "nla, condition estimation, qrd"
}
@article{bipl:90,
author = "C. H. Bischof and D. J. Pierce and J. G. Lewis",
year = "1990",
title = "Incremental Condition Estimation for Sparse Matrices",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "644--659",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition estimation, sparse"
}
@techreport{bipt:90,
author = "C. H. Bischof and C.-T. Pan and P. T. P. Tang",
year = "1990",
title = "Stable {Cholesky} Up- and Downdating Algorithms
for Systolic and SIMD Architectures",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Preprint",
number = "MCS-P167-00790",
kwds = "nla, prll, updating, Cholesky decomposition,
systolic, simd"
}
@article{bisc:91,
author = "C. H. Bischof",
year = "1991",
title = "A Parallel {QR}~Factorization Algorithm with
Controlled Local Pivoting",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "36--57",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, qrd, rank determination"
}
@article{biha:91,
author = "C. H. Bischof and P. C. Hansen",
year = "1991",
title = "Structure Preserving and Rank-Revealing {QR}~Factorizations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "1332--1350",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, qrd, sparse, rank determination"
}
@article{bish:91,
author = "C. H. Bischof and G. M. Shroff",
year = "1991",
title = "On Updating Signal Subspaces",
journal = "IEEE Transactions on Signal Processing",
volume = "40",
pages = "96--105",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, signal processing, rank determination"
}
@techreport{biha:91a,
author = "C. H. Bischof and P. C. Hansen",
year = "1991",
title = "A Block Algorithm for Computing
Rank-Revealing {QR}-Factorizations",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Reprot",
number = "MCS-P251-0791",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, qrd, rank determination, block algorithm"
}
@book{bifh:75,
author = "Yvonne M. M. Bishop and Stephen E. Fienberg
and Paul W. Holland",
year = "1975",
title = "Discrete Multivariate Analysis",
publisher = "MIT Press",
address = "Cambridge, Massachusetts",
kwds = "book, stat, log-linear model, categorical data,
multivariate analysis"
}
@techreport{bitn:79,
author = "James R. Bitner",
year = "1979",
title = "Algorithms for Storing Matrices on Disk to Minimize Access Time",
institution = "Department of Computer Science,
The University of Texas at Austin",
type = "Technical Report",
number = "TR-99",
kwds = "nla, memory hierarchy"
}
@article{bidh:84,
author = "Dina Bitton and David J. DeWitt and David K. Hsiao and
Jaishankar Menon",
year = "1984",
title = "A Taxonomy of Parallel Sorting",
journal = "Computing Surveys",
volume = "16",
pages = "287-318",
kwds = "prll, sorting"
}
-bj-
@article{bjer:51,
author = "A. Bjerhammer",
year = "1951",
title = "Rectangular Reciprocal Matrices with Special Reference
to Geodetic Calculations",
journal = "Bulletin G\'eod\'esique",
volume = "52",
pages = "118-220",
kwds = "la, ginv, lsq"
}
@article{bjor:67,
author = "{\AA}. Bj{\"o}rck",
year = "1967",
title = "Solving Linear Least Squares Problems by {Gram--Schmidt}
Orthogonalization",
journal = "BIT",
volume = "7",
pages = "1-21",
kwds = "nla, lsq, qrd, Gram-Schmidt algorithm"
}
@article{bjgo:67,
author = "{\AA}. Bj{\"o}rk and G. H. Golub",
year = "1967",
title = "Iterative Refinement of Linear Least Squares Solution
by Householder Transformation",
journal = "BIT",
volume = "7",
pages = "322--337",
kwds = "nla, lsq, iterative refinement, Householder transformation"
}
@article{bjor:67a,
author = "{\AA}. Bj{\"o}rck",
year = "1967",
title = "Iterative Refinement of Linear Least Squares Solutions {I}",
journal = "BIT",
volume = "7",
pages = "257--278",
kwds = "nla, lsq, iterative refinement"
}
@article{bjor:67b,
author = "{\AA}. Bj{\"o}rck",
year = "1967",
title = "Contribution no.~22. {Iterative} Refinement of Linear Least
Squares Solutions by {Householder} Transformations",
journal = "BIT",
volume = "7",
pages = "322--337",
kwds = "nla, lsq, iterative refinement, Householder transformation"
}
@article{bjor:68,
author = "{\AA}. Bj{\"o}rck",
year = "1968",
title = "Iterative Refinement of Linear Least Squares Solutions {II}",
journal = "BIT",
volume = "8",
pages = "8-30",
kwds = "nla, lsq, iterative refinement"
}
@article{bjpe:70,
author = "{\AA}. Bj{\"o}rck and V. Pereyra",
year = "1970",
title = "Solution of {V}andermonde Systems of Equations",
journal = "Mathematics of Computation",
volume = "24",
pages = "893--903",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Vandermonde matrix, linear system"
}
@article{bjor:71,
author = "{\AA}. Bj{\"o}rck and C. Bowie",
year = "1971",
title = "An Iterative Algorithms for Computing the Best Estimate of
an Orthogonal Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "358--364",
kwds = "nla, svd, orthogonal matrix"
}
@article{bjel:73,
author = "{\AA}. Bj{\"o}rck and Tommy Elfving",
year = "1973",
title = "Algorithms for Confluent {Vandermonde} Systems",
journal = "Numerische Mathematik",
volume = "21",
pages = "130--137",
kwds = "nla, Vandermonde matrix"
}
@article{bjgo:73,
author = "{\AA}. Bj{\"o}rck and G. H. Golub",
year = "1973",
title = "Numerical Methods for Computing Angles between Linear Subspaces",
journal = "Mathematics of Computation",
volume = "27",
pages = "579-594",
kwds = "math, nla, gsvd, canonical angles, subspace metric"
}
@inproceedings{bjor:76,
author = "{\AA}. Bj{\"o}rck",
year = "1976",
title = "Methods for Sparse Least Squares Problems",
pages = "177-199",
booktitle = "Sparse Matrix Computations",
editor = "J.R. Bunch and D. J. Rose",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{bjor:78,
author = "{\AA}. Bj{\"o}rck",
year = "1978",
title = "Comment on the Iterative Refinement of Least Squares Solutions",
journal = "Journal of the American Statistical Association",
volume = "73",
pages = "161--166",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, iterative refinement"
}
@inproceedings{bjor:79,
author = "{\AA}. Bj{\"o}rck",
year = "1979",
title = "{SSOR} Preconditioning Methods for Sparse Least Squares Problems",
pages = "21--25",
booktitle = "In Proceedings of the Computer Science and Statistics
12th Annual Symposium on the Interface",
publisher = "University of Waterloo, Canada",
address = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, relaxation, preconditioning"
}
@article{bjel:79,
author = "{\AA}. Bj{\"o}rck and Tommy Elfving",
year = "1979",
title = "Accelerated Projection Methods for Computing Pseudoinverse
Solutions of Systems of Linear Equations",
journal = "BIT",
volume = "19",
pages = "145--163",
kwds = "nla, ginv, linear system, iter"
}
@techreport{bjel:79,
author = "{\AA}. Bj{\"o}rck and L. Eld\'en",
year = "1979",
title = "Methods in numerical algebra for ill-posed problems",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MAT-R-1979-33",
kwds = "nla, linear system, regularization, ill-posed problem"
}
@article{bjgu:80,
author = "{\AA}. {Bj\"orck} and I. S. Duff",
year = "1980",
title = "A Direct Method for the Solution of Sparse Linear Least Squares
Problems",
journal = "Linear Algebra and Its Applications",
volume = "34",
pages = "43-68",
kwds = "nla, lsq, sparse"
}
@book{bjpl:81,
author = "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider",
year = "1981",
title = "Large--Scale Matrix Problems",
publisher = "North-Holland",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, sparse"
}
@article{bjha:83,
author = "{\AA}. Bj{\"o}rck and S. Hammarling",
year = "1983",
title = "A {S}chur Method for the Square Root of a Matrix",
journal = "Linear Algebra and Its Applications",
volume = "52/53",
pages = "127--140",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix square root"
}
@article{bjor:84,
author = "{\AA}. Bj{\"o}rck",
year = "1984",
title = "A General Updating Algorithm for Constrained Linear Least Squares
problems",
journal = " SIAM Journal on Scientific and Statistical Computing",
volume = "5",
pages = "394--402.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse, updating, constraints"
}
@article{bjor:87,
author = "{\AA}. Bj{\"o}rck",
year = "1987",
title = "Stability Analysis of the Method of Seminormal Equations",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "31--48",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lsq, rounding error, normal equations"
}
@techreport{bjor:87a,
author = "{\AA}. Bj{\"o}rck",
year = "1987",
title = "Least Squares Methods",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Working paper",
number = "",
note = "To appear in {\it Handbook of Numerical Analysis, V.1:
Solution of Equations in $R^n$}, P. G. Ciarlet and J. L.
Lions editors, Elsevier, North Holland",
kwds = "math, na, nla, lsq, regr"
}
@book{bjor:88,
author = "{\AA}. Bj{\"o}rck",
year = "1988",
title = "Solution of Equations in {$R^N$}",
series = "Least Squares Methods: Handbook of Numerical Analysis",
volume = "1",
publisher = "North-Holland",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, lsq"
}
@techreport{bjor:88a,
author = "{\AA}. Bj{\"o}rck",
year = "1988",
title = "Error Analysis of Least Squares Algorithms",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MAT-R-1988-22",
kwds = "nla, lsq, rounding error, pert"
}
@article{bjor:88b,
author = "{\AA}. Bj{\"o}rck",
year = "1988",
title = "A Bidiagonalization Algorithm for Solving Ill-Posed System
of Linear Equations",
journal = "BIT",
volume = "28",
pages = "659--670",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, sparse, Lanczos algorithm, bidiagonalization,
ill-posed system, regularization"
}
@article{bjor:88b,
author = "{\AA}. Bj{\"o}rck",
year = "1988",
title = "A Direct Method for Sparse Least Squares Problems with lower and
Upper Bounds",
journal = " Numerische Mathematik",
volume = "54",
pages = "19--32",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints"
}
@techreport{bjor:89,
author = "{\AA}. Bj{\"o}rck",
year = "1989",
title = "Componentwise Backward Errors and Condition Estimates for
Linear Least Square Problems",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MATH-R-1989-13",
kwds = "la, nla, lsq, pert, backward perturbation"
}
@techreport{bjor:90,
author = "{\AA}. Bj{\"o}rck",
year = "1990",
title = "Error Analysis of the Modified {Gram--Schmidt} Method
for Solving Underdetermined Linear Systems",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MAT-R-1990-06",
kwds = "nla, Gram-Schmidt algorithm, rounding error"
}
@inproceedings{bjor:90a,
author = "{\AA}. Bj{\"o}rck",
year = "1990",
title = "Iterative Refinement and Reliable Computing",
pages = "249--266",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. J. Hammarling",
publisher = "Clarendon Press",
address = "Oxford",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, iterative refinement"
}
@unpublished{bjor:90b,
author = "{\AA}. Bj{\"o}rck",
year = "1990",
title = "The Householder Symposium: Meeting on Numerical Algebra",
note ="Abstracts of the Symposium. Compiled by {\AA}ke Bj{\"o}rk,
Department of Mathematics, Link{\"o}ping University",
kwds = "nla, Householder Symposium"
}
@incollection{bjor:90c,
author = "{\AA}. Bj{\"o}rck",
year = "1990",
title = "Least Squares Methods",
editor = "P. G. Ciarlet and J. L. Lions",
booktitle = "Handbook of Numerical Analysis",
publisher = "Elsevier/North Holland",
volume = "I: Finite Difference Methods-Solution of Equations in $R^n$",
address = "Amsterdam",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq"
}
@inproceedings{bjor:91,
author = "{\AA}. Bj{\"o}rck",
year = "1991",
title = "Error Analysis of Least Squares Algorithms",
pages = "41--73",
booktitle = "Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms",
series = "NATO ASI Series",
editor = "G. H. Golub and P. Van Dooren",
publisher = "Springer",
address = "Berlin",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, rounding error, signal processing"
}
@article{bjpa:92,
author = "{\AA}. Bj{\"o}rck and C. C. Paige",
year = "1992",
title = "Loss and Recapture of Orthogonality in the Modified {Gram-Schmidt}
Algorithm",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "13",
pages = "176--190",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, orthogonalization, Gram-Schmidt algorithm, rounding error"
}
@article{bjor:91a,
author = "{\AA}. Bj{\"o}rck",
year = "1991",
title = "Component-wise Perturbation Analysis and Errors Bounds for
Linear Least Square Solutions",
journal = "BIT",
volume = "31",
pages = "238--244",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, structured perturbation, pert"
}
@techreport{bjor:91b,
author = "{\AA}. Bj{\"o}rck",
year = "1991",
title = "Pivoting and Stability in the Augmented System Method",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Report",
number = "LiTH-MAT-R-1991-30",
kwds = "nla, rounding error, lsq"
}
-bk- -bl-
@article{blst:74,
author = "M. M. Blevins and G. W. Stewart",
year = "1974",
title = "Calculating Eigenvectors of Diagonally Dominant
Matrices",
journal = "Journal of the ACM",
volume = "21",
pages = "261--271",
kwds = "nla, eig, diagonal dominance"
}
@article{blue:78,
author = "J. L. Blue",
year = "1978",
title = "A Portable Fortran Program to Find the Euclidean Norm of a Vector",
journal = "Transactions on Mathematical Software",
volume = "4",
pages = "15-23",
kwds = "nla, blas, software, norm"
}
@article{blum:67,
author = "E. K. Blum",
year = "1967",
title = "The Computation of Eigenvalues and Eigenvectors of a
Completely Continuous Self-Adjoint Operator",
journal = "J. Comput. Syst. Sci.",
volume = "1",
pages = "362--370",
kwds = "nla, eig, sparse"
}
-bm- -bn- -bo-
@techreport{bobu:63,
author = "D. Bogert and W. R. Burris",
year = "1963",
title = "Comparison of Least Squares Algorithms",
institution = "Neutron Physics Division,
Oak Ridge National Laboratory",
type = "Report",
number = "ORNL-3499",
note = "Vol. 1, Sec. 5.5",
kwds = "nla, lsq, qrd"
}
@article{bobs:87,
author = "P. T. Boggs and R. H. Byrd and R. B. Schnabel",
year = "1987",
title = "A Stable and Efficient Algorithm for Nonlinear
Orthogonal Regression",
journal = " SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "1052--1078",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{boht:75,
author = "Z. Bohte",
year = "1975",
title = "Bounds for Rounding Errors in the {G}aussian Elimination for Band
Systems",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "16",
pages = "133--142",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, band matrix, rounding error"
}
@article{bobr:86,
author = "A. Bojanczyk and R. P. Brent",
year = "1986",
title = "Parallel Solution of Certain {Toeplitz} Least-Squares
Problems",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "43-60",
kwds = "nla, systolic, prll, Toeplitz matrix, lsq"
}
@article{bobh:86,
author = "A. Bojanczyk and R. P. Brent and F. de Hoog",
year = "1986",
title = "{QR} Factorization of Toeplitz Matrices",
journal = "Numerische Mathematik",
volume = "49",
pages = "81--94",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, Toeplitz matrix"
}
@article{bobv:87,
author = "A. Bojanczyk and R. P. Brent and P. Van Dooren and F. de Hoog",
year = "1987",
title = "A Note on Downdating the {Cholesky} Factorization",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "210--221",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Cholesky decomposition, updating"
}
@article{bogu:84,
author = "D. L. Boley and G. H. Golub",
year = "1984",
title = "The {Lanczos--Arnoldi} Algorithm and Controllability",
journal = "Systems and Control Letters",
volume = "4",
pages = "317--324",
kwds = "nla, controllability, Lanczos algorithm, Arnoldi's method"
}
@article{bolu:86,
author = "D. L. Boley and W.-S. Lu",
year = "1986",
title = "Measuring How Far a Controllable System is from an
Uncontrollable One",
journal = "IEEE Transactions on Automatic Control",
volume = "AC-31",
pages = "249--251",
kwds = "nla, condition, controllability"
}
@inproceedings{bogs:91,
author = "E. C. Boman and M. F. Griffen and G. W. Stewart",
year = "1991",
title = "Direction of Arrival and The Rank-Revealing URV Decomposition",
booktitle = "Procedings of ACASSP-91",
publisher = "IEEE",
address = "Washington, DC",
kwds = "nla, signal processing, direction of arrival, urvd"
}
@article{bobo:88,
author = "A. D. Booth and I. J. M. Booth",
year = "1988",
title = "A Note on the Progressive Calculation of the Mean
and Variance",
journal = "Journal of Computational Physics",
volume = "77",
pages = "537--539",
kwds = "stat, mean, variance, update, software"
}
@article{boot:70,
author = "J. Boothroyd",
year = "1970",
title = "The {QR}~Algorithm for Symmetric Tridiagonal Matrices
Using a Semi-implicit Shift of the Orgin",
journal = "Australian Computer Journal",
volume = "2",
pages = "55--60",
kwds = "nla, eig, QR algorithm, tridiagonal matrix, symmetric matrix"
}
@article{borc:1857,
author = "C. W. Borchart",
year = "1857",
title = " {Bemerkung \"uber die beiden vorstehenden Aufs\"atze}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "53",
pages = "281-283",
kwds = "la, inertia, Sylvester-Jacobi inertia theorem"
}
@article{bors:70,
author = "W. B{\"o}rsch-Supan",
year = "1970",
title = " {Residuenabsch\"atzung f\"ur Polynom-Nullstellen
Mittels Lagrange-Interpolation}",
journal = "Numerische Mathematik",
volume = "287--296",
pages = "287--296",
kwds = "nlop, polynomial, pert, interpolation"
}
@book{bood:71,
author = "T. L. Boullion and P. L. Odell",
year = "1971",
title = "Generalized Inverse Matrices",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, la, ginv"
}
@article{bmpw:66,
author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H. Wilkinson",
year = "1966",
title = "Solution of Real and Complex Systems of Linear Equations",
journal = "Numerische Mathematik",
volume = "8",
pages = "217--234",
note = "Also in \cite[pp.92--110]{wire:71}.",
kwds = "nla, lud, linear system, software"
}
@article{bmrw:68,
author = "H. J. Bowdler and R. S. Martin and C. Reinsch and
J. H. Wilkinson",
year = "1968",
title = "The {QR}~and {LR}~Algorithms for Symmetric Matrices",
journal = "Numerische Mathematik",
volume = "11",
pages = "293--306",
note = "Also in \cite[pp.227--240]{wire:71}.",
kwds = "nla, eig, QR algorithm, symmetric matrix, software"
}
@article{bohu:59,
author = "G. E. P. Box and J. S. Hunter",
year = "1959",
title = "Condensed Calculations for Evolutionary Operation Programs",
journal = "Technometrics",
volume = "1",
pages = "77-95",
kwds = "stat, na"
}
@book{boye:68,
author = "C. B. Boyer",
year = "1968",
title = "A History of Mathematics",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, math, history"
}
@book{bbdg:87,
author = "J. Boyle and R. Butler and T. Disz and B. Glickfield and E. Lusk
and R. Overbeek and J. Patterson and R. Stevens",
year = "1987",
title = "Portable Programs for Parallel Processors",
publisher = "Holt, Rinehart and Winston",
note = "Cited in \cite{govl:89}.",
kwds = "book, cs, prll"
}
-bp- -bq- -br-
@article{brfl:66,
author = "W. W. Bradbury and R. Fletcher",
year = "1966",
title = "New Iterative Methods for Solution of the Eigenproblem",
journal = "Numerische Mathematik",
volume = "9",
pages = "259--267",
kwds = "nla, eig, sparse, conjugate gradients"
}
@article{brsr:79,
author = "R. A. Bradley and S. S. Srivastva",
year = "1979",
title = "Correlation in Polynomial Regression",
journal = "American Statistician",
volume = "33",
pages = "11-14",
kwds = "stat, regr, correlation, polynomial"
}
@article{brps:86,
author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
year = "1986",
title = "The construction of Preconditioners for Elliptic Problems by
Substructuring {I}",
journal = "Mathematics of Computation",
volume = "47",
pages = "103--134",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning"
}
@article{brps:86a,
author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz",
year = "1986",
title = "The construction of Preconditioners for Elliptic Problems by
Substructuring {II}",
journal = "Mathematics of Computation",
volume = "49",
pages = "1--17",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning"
}
@phdthesis{bram:89,
author = "R. B. Bramley",
year = "1989",
title = "Row Projection Methods for Linear Systems",
school = "Center for Supercomputing Research and Development,
University of Illinois",
kwds = "nla, sparse, linear system, Kaczmarz's method, projection method,
Cimmino's method"
}
@techreport{brsa:90,
author = "R. Bramley and A. Sameh",
year = "1990",
title = "Row Projection Methods for Large Nonsymmetric Linear Systems",
institution = "Center for Supercomputing Research and Development",
adress = "University of Urbana, Illinois",
type = "Report",
number = "No. 957",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, sparse, prll, projection method"
}
@article{brpa:86,
author = "A. Brass and G. S. Pawley",
year = "1986",
title = "Two and Three Dimensional {FFT}s on Highly
Parallel Compters",
journal = "Parallel Computing",
volume = "3",
pages = "167-184",
kwds = "prll, systolic, fft, fast algorithm"
}
@article{brro:69,
author = "Alfred Brauer and Hans Rohrbach",
year = "1969",
title = " {Einige Anwendungen der Matrizentheorie auf
algebraische Gleichungen}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "236",
pages = "11--25",
kwds = "la, nlop, eig, pert, polynomial"
}
@techreport{bren:70,
author = "R. P. Brent",
year = "1970",
title = "Algorithms for Matrix Multiplication",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "STAN-CS-70-157",
kwds = "nla, matrix multiplication, fast algorithm, rounding error"
}
@article{bren:70a,
author = "R. P. Brent",
year = "1970",
title = "Error Analysis of Algorithms for Matrix Multiplication
and Triangular Decomposition using Winograd's Identity",
journal = "Numerische Mathematik",
volume = "16",
pages = "145--156",
note = "Cited in \cite{high:89b}",
kwds = "nla, matrix multiplication, fast algorithm, rounding error"
}
@article{bren:72,
author = "R. P. Brent",
year = "1972",
title = "On the {Davidenko--Branin} Method for Solving Simultaneous
Nonlinear Equations",
journal = "IBM Journal of Research and Development",
volume = "16",
pages = "434--436",
kwds = "nlop"
}
@article{bren:73,
author = "R. P. Brent",
year = "1973",
title = "Some Efficient Algorithms for Solving Systems of
Nonlinear Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "327--344",
kwds = "nlop"
}
@article{brlu:8?,
author = "R. P. Brent and F. T. Luk",
year = "19??",
title = "A Systolic Array for the Linear-Time Solution of {Toeplitz}
Systems of Equations",
journal = "Journal of VLSI and Computer Systems",
volume = "1",
pages = "1--22",
kwds = "nla, prll, Toeplitz matrix, systolic"
}
@article{brlu:85,
author = "R. P. Brent and F. T. Luk",
year = "1985",
title = "The Solution of Singular-Value and Symmetric Eigenvalue
Problems on Multiprocessor Arrays",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "6",
pages = "69--84",
kwds = "nla, prll, svd, eig, symmetric matrix, systolic"
}
@article{brlv:8?,
author = "R. P. Brent and F. T. Luk and Van Loan, C.",
year = "198?",
title = "Computation of the Singular Value Decomposition
Using Mesh-Connected Processors",
journal = "Journal of VLSI and Computer Systems",
volume = "1",
pages = "242--270",
kwds = "nla, prll, svd, systolic"
}
@book{brez:80,
author = "C. Brezinski",
year = "1980",
title = "Pad\'e-Type Approximations and General Orthogonal
Polynomials",
publisher = "Birkh{\"a}user",
address = "Basel",
kwds = "book, na, nla, Pade table, orthogonal polynomial"
}
@article{broc:81,
author = "H. K. Brock and B. J. Brooks and F. Sullivan",
year = "1981",
title = "Diamond a Sorting Method for Vector Machines",
journal = "BIT",
volume = "21",
pages = "142--152",
kwds = "prll, sorting"
}
@article{brpo:75,
author = "K. W. Brodlie and M. J. D. Powell",
year = "1975",
title = "On the Convergence of Cyclic {J}acobi Methods",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "15",
pages = "279--287",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Jacobi's method"
}
@article{brjo:74,
author = "O. E. Br{\o}nlund and L. Johnsen",
year = "1974",
title = "{QR}-Factorization of Partitioned Matrices",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "3",
pages = "143-172",
kwds = "nla, qrd"
}
@article{broo:87,
author = "E. D. Brooks III",
year = "1987",
title = "A Butterfly Processor-Memory Interconnection
for a Vector Processing Environment",
journal = "Parallel Computing",
volume = "4",
pages = "103-110",
kwds = "prll, shared memory, vect"
}
@article{brde:68,
author = "K. M. Brown and J. E. Dennis",
year = "1968",
title = "On {Newton}-Like Iteration Functions: General Convergence
Theorems and a Specific Algorithm",
journal = "Numerische Mathematik",
volume = "12",
pages = "186--191",
kwds = "nlop, Newton's method"
}
@article{brkr:74,
author = "G. F. Brown and J. B. Kadane and J. G. Ramage",
year = "1974",
title = "The Asymptotic Bias and Mean-Squared Error of Double
{$K$}-class Estimators when the Distrubances are Small",
journal = "International Economic Review",
volume = "15",
pages = "667--679",
kwds = "stat, regr, pert, eriv"
}
@article{brow:28,
author = "E. T. Browne",
year = "1928",
title = "The Characteristic Equations of a Matrix",
journal = "Bulletin of the American Mathematical Society",
volume = "34",
pages = "363-368",
kwds = "la, eig"
}
@article{brow:30,
author = "E. T. Browne",
year = "1930",
title = "The Characteristic Roots of a Matrix",
journal = "Bulletin of the American Mathematical Society",
volume = "36",
pages = "708-710",
kwds = "la, eig"
}
@inproceedings{brow:85,
author = "J. C. Browne",
year = "1985",
title = "Formulation and Programming of Parallel Computations:
A Unified Approach",
booktitle = "Proceedings of the 1978 International Conference
on Parallel Processing",
editor = "D. Degroot",
pages = "624-631",
publisher = "IEEE Computer Society Press",
address = "Wahsington, DC",
kwds = "prll"
}
@book{brow:65,
author = "K. A. Brownlee",
year = "1965",
title = "Statistical Theory and Methodology in Science and Engineering",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat"
}
@article{broy:65,
author = "C. G. Broyden",
year = "1965",
title = "A Class of Methods for Solving Nonlinear Simultaneous Equations",
journal = "Mathematics of Computation",
volume = "19",
pages = "577--593",
kwds = "nlop, quasi-Newton"
}
@article{broy:67,
author = "C. G. Broyden",
year = "1967",
title = "Quasi-{Newton} Methods and their Application to Function
Minimization",
journal = "Mathematics of Computation",
volume = "21",
pages = "368--381",
kwds = "nlop, quasi-Newton"
}
@article{broy:69,
author = "C. G. Broyden",
year = "1969",
title = "A New Method of Solving Nonlinear Simultaneous Equations",
journal = "Computer Journal",
volume = "12",
pages = "1969",
kwds = "nlop, quasi-Newton, continuation"
}
@article{broy:70,
author = "C. G. Broyden",
year = "1970",
title = "The Convergence of Single-Rank Quasi-{Newton} Methods",
journal = "Mathematics of Computation",
volume = "24",
pages = "365--382",
kwds = "nlop, quasi-Newton"
}
@article{broy:73,
author = "C. G. Broyden",
year = "1973",
title = "Some Condition Number Bounds for the {G}aussian Elimination
Process",
journal = "Journal of the Institute of Mathematics and Its Applications",
volume = "12",
pages = "273--286",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, condition"
}
@unpublished{brsc:82,
year = "1982",
author = "R. A. Brualdi and H. Schneider",
title = "Determinantal Identities: {Gauss, Schur, Cauchy, Sylvester,
Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley}",
note = "Manuscript. Department of Mathematics, University of Wisconsin",
kwds = "la, determinant, Schur complement"
}
@book{brba:80,
author = "S. C. Bruell and G. Balbo",
year = "1980",
title = "Computational Algorithms for Closed Queueing Networks",
publisher = "North Holland",
address = "New York",
kwds = "book, la, queue, Markov chain"
}
-bs- -bt- -bu-
@article{buck:74,
author = "A. Buckley",
year = "1974",
title = "A Note on Matrices {$A = 1 + H$}, {$H$} Skew-Symmetric",
journal = "Zeitschrift fur Angewandte Mathematik und Mechanik",
volume = "54",
pages = "125--126",
note = "Cited in \cite{govl:89}.",
kwds = "la, skew-symmetric matrix"
}
@article{buck:77,
author = "A. Buckley",
year = "1977",
title = "On the Solution of Certain Skew-Symmetric Linear Systems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "14",
pages = "566--570",
note = "Cited in \cite{govl:89}.",
kwds = "la, linear system, skew-symmetric matrix"
}
@article{bupa:71,
author = "J. R. Bunch and B. N. Parlett",
year = "1971",
title = "Direct Methods for Solving Symmetric Indefinite Systems
of Linear Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "639--655",
kwds = "nla, lud, indefinite system, linear system, symmetric matrix"
}
@article{bunc:71,
author = "J. R. Bunch",
year = "1971",
title = "Analysis of the Diagonal Pivoting Method",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "656--680",
kwds = "nla, lud, indefinite system, linear system, pivoting,
symmetric matrix"
}
@article{bunc:71a,
author = "J. R. Bunch",
year = "1971",
title = "Equilibration of Symmetric Matrices in the Max-Norm",
journal = "Journal of the ACM",
volume = "18",
pages = "566--572",
kwds = "nla, scaling, symmetric matrix"
}
@article{bunc:74,
author = "J. R. Bunch",
year = "1974",
title = "Partial Pivoting Strategies for Symmetric Matrices",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "521--528",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting, symmetric matrix"
}
@proceedings{buro:76,
editor = "J. R. Bunch and D. J. Rose",
year = "1976",
title = "Sparse Matrix Computations",
publisher = "Academic Press",
address = "New York",
kwds = "math, nla, sparse"
}
@article{bukp:76,
author = "J. R. Bunch and L. Kaufman and B. Parlett",
year = "1976",
title = "Decomposition of a Symmetric Matrix",
journal = "Numerische Mathematik",
volume = "27",
pages = "95--109",
kwds = "nla, lud, indefinite system, linear system, symmetric matrix"
}
@article{buka:77,
author = "J. R. Bunch and L. Kaufman",
year = "1977",
title = "Some Stable Methods for Calculating Inertia and Solving Symmetric
Linear Systems",
journal = "Mathematics of Computation",
volume = "31",
pages = "163-179",
kwds = "math, nla, linear system, inertia, symmetric matrix"
}
@article{buns:78,
author = "J. R. Bunch and C. P. Nielsen and D. C. Sorensen",
year = "1978",
title = "Rank One Modification of the Symmetric Eigenproblem",
journal = "Numerische Mathematik",
volume = "31",
pages = "31--48",
kwds = "nla, eig, updating, symmetric matrix"
}
@article{buni:78,
author = "J. R. Bunch and C. P. Nielsen",
year = "1978",
title = "Updating the Singular Value Decomposition",
journal = "Numerische Mathematik",
volume = "31",
pages = "111--129",
kwds = "nla, svd, updating"
}
@article{bunc:82,
author = "J. R. Bunch",
year = "1982",
title = "A Note on the Stable Decomposition of Skew Symmetric Matrices",
journal = "Mathematics of Computation",
volume = "158",
pages = "475--480",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, skew-symmetric matrix"
}
@article{bunc:85,
author = "J. R. Bunch",
year = "1985",
title = "Stability of Methods for Solving {T}oeplitz Systems of Equations",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "6",
pages = "349--364",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, Toeplitz matrix, linear system"
}
@article{bunc:87,
author = "J. R. Bunch",
year = "1987",
title = "The Weak and Strong Stability of Algorithms in Numerical Linear
Algebra",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "49--66",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pert, rounding error"
}
@article{budv:89,
author = "J. R. Bunch and J. Demmel and Van Loan, C. F.",
year = "1989",
title = "The Strong Stability of Algorithms for Solving Symmetric
Linear Systems",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "10",
pages = "494--499",
kwds = "nla, pert, backward perturbation, symmetric matrix"
}
@techreport{bune:69,
author = "O. Buneman",
year = "1969",
title = "A Compact Non-Iterative {P}oisson Solver",
institution = "Institute for Plasma Research",
address = "Stanford University, Stanford, CA",
Number = 294,
note = "Cited in \cite{govl:89}.",
kwds = "nla, direct Poisson solver"
}
@article{buns:4b,
author = "A. Bunse-Gerstner",
year = "1984",
title = "An Algorithm for the Symmetric Generalized Eigenvalue Problem",
journal = "Linear Algebra and its Applications",
volume = "58",
pages = "43--68",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, symmetric matrix"
}
@article{bgbm:92,
author = "A. Bunse-Gerstner and R. Byers and V. Mehrmann",
year = "1992",
title = "A Chart of Numerical Methods for Structured Eigenvalue
Problems",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "419--453",
kwds = "nla, eig, J-symmetric matrix, J-orthogonal matrix"
}
@phdthesis{bure:70,
author = "H. J. Burema",
year = "1970",
title = "A Geometric Proof of Convergence of the {QR}~Method",
school = "University of Groningen",
kwds = "nla, eig, QR algorithm"
}
@article{bude:75,
author = "J. C. P. Bus and T. J. Dekker",
year = "1975",
title = "Two Efficient Algorithms with Guaranteed Convergence
for Finding a Zero of a Function",
journal = "ACM Transactions on Mathematical Software",
volume = "1",
pages = "330--345",
kwds = "nlop"
}
@article{busi:65,
author = "P. Businger",
year = "1965",
title = "Algorithm 253: Eigenvalues of a Real Symmetric Matrix
by the {QR}~Method",
journal = "Communication of the ACM",
volume = "8",
pages = "217--219",
kwds = "nla, eig, QR algorithm, symmetric matrix"
}
@article{bugo:65,
author = "P. Businger and G. H. Golub",
year = "1965",
title = "Linear Least Squares Solutions by {Householder} Transformations",
journal = "Numerische Mathematik",
volume = "7",
pages = "269--276",
note = "Also in \cite[pp.111-118]{wire:71}",
kwds = "nla, lsq, qrd, Householder transformation, software"
}
@article{busi:68,
author = "P. Businger",
year = "1968",
title = "Matrices Which Can be Optimally Scaled",
journal = "Numerische Mathematik",
volume = "12",
pages = "346--248",
kwds = "nla, condition, scaling"
}
@article{bugo:69,
author = "P. Businger and G. H. Golub",
year = "1969",
title = "Algorithm 358, Singular Value Decomposition of a Complex
Matrix",
journal = "Communications of the ACM",
volume = "12",
pages = "564--565",
kwds = "nla, svd, software"
}
@article{busi:69,
author = "P. A. Businger",
year = "1969",
title = "Reducing a Matrix to {H}essenberg Form",
journal = "Mathematics of Computation",
volume = "23",
pages = "819--821",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Hessenberg matrix"
}
@article{busi:71,
author = "P. A. Businger",
year = "1971",
title = "Monitoring the Numerical Stability of {G}aussian Elimination",
journal = "Numerische Mathematik",
volume = "16",
pages = "360--361",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, rounding error"
}
@article{busi:71a,
author = "P. A. Businger",
year = "1971",
title = "Numerically Stable Deflation of {H}essenberg and Symmetric
Tridiagonal Matrices",
journal = "{BIT}",
volume = "11",
pages = "262--270",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Hessenberg matrix, tridiagonal matrix, deflation"
}
@article{bugn:70,
author = "B. L. Buzbee and G. H. Golub and C. W. Nielson",
year = "1970",
title = "On Direct Methods for Solving {Poisson's} Equation",
journal = "SIAM Journal on Numerical Analysis",
volume = "7",
pages = "627--656",
kwds = "nla, pde, direct Poisson solver, sparse"
}
@article{bdgg:71,
author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub",
year = "1971",
title = "The Direct Solution of the Discrete {P}oisson Equation on Irregular
Regions",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "8",
pages = "722--736",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pde, direct Poisson solver, sparse"
}
@article{budo:74,
author = "B. L. Buzbee and F. W. Dorr",
year = "1974",
title = "The Direct Solution of the Biharmonic Equation on Rectangular
Regions and the {P}oisson Equation on Irregular Regions",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "753--763",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pde, fast Poisson solver, sparse"
}
@article{buzb:86,
author = "B. L. Buzbee",
year = "1986",
title = "A Strategy for Vectorization",
journal = "Parallel ",
volume = "3",
pages = "187--192",
note = "Cited in \cite{govl:89}.",
kwds = "cs, vect"
}
-bv- -bw- -bx- -by-
@phdthesis{byer:83,
author = "R. Byers",
year = "1983",
title = "{H}amiltonian and Symplectic Algorithms for the Algebraic {R}iccati
Equation",
school = "Center for Applied Mathematics, Cornell University",
address = "Ithaca, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, J-symmetric matrix, J-orthogonal matrix, Riccati equation"
}
@article{byer:84,
author = "R. Byers",
year = "1984",
title = "A {L}inpack-Style Condition Estimator for the Equation
{$AX - XB^{T} = C$}",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-29",
pages = "926--928",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition estimation, Sylvester equation, matrix equation"
}
@article{byna:87,
author = "R. Byers and S. G. Nash",
year = "1987",
title = "On the Singular Vectors of the {L}yapunov Operator",
journal = "{SIAM} Journal on Algebraic and Discrete Methods",
volume = "8",
pages = "59--66",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, Lyapunov equation, matrix equation"
}
@article{bysc:86,
author = "R. H. Byrd and R. B. Schnabel",
year = "1986",
title = "Continuity of the Null Space Basis and Constrained Optimization",
journal = "Mathematical Programming",
volume = "35",
pages = "32--41",
kwds = "nla, nlop, null space, constraints"
}
-bz-
-ca-
@inproceedings{cali:86,
author = "D. A. Calihan",
year = "1986",
title = "Block-Oriented, Local-Memory-Based Linear Equation Solution on the
{C}ray-2: Uniprocessor Algorithms",
booktitle = "Proceedings of the 1986 Conference on Parallel Processing",
pages = "375--378",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, linear system, vect"
}
@article{came:75,
author = "S. L. Campbell and C. D. Meyer",
year = "1975",
title = "Continuity Properties of the Drazin Pseudoinverse",
journal = "Linear Algebra and Its Applications",
volume = "10",
pages = "77--83",
kwds = "la, pert, eig, ginv, Drazin generalized inverse"
}
@article{cast:85,
author = "W. L. Cao and W. J. Stewart",
year = "1985",
title = "Iterative Aggregation/Disaggregation Techniques for
Nearly Uncoupled {Markov} Chains",
journal = "Journal of the ACM",
volume = "32",
pages = "702-719",
kwds = "la, nla, Markov chain, aggregation, iter"
}
@incollection{cauc:1821,
author = "A. L. Cauchy",
year = "1821",
title = "Cours d'analyse de l'\'Ecole Royale Polytechnique",
booktitle = "Oeuvres Compl\'etes (II\,$^e$ S\'erie)",
volume = "3",
kwds = "la, Cauchy inequality, history"
}
@incollection{cauc:1829,
author = "A. L. Cauchy",
year = "1829",
title = "Sur l'\'equation \'a l'aide de laquelle on d\'etermine les
in\'egalit\'es s\'eculaires des mouvements des plan\`etes",
booktitle = "Oeuvres Compl\'etes (II\,$^e$ S\'erie)",
volume = "9",
kwds = "la, history, eig, Cauchy interlacing theorem, symmetric matrix"
}
@article{cauc:1837,
author = "A. Cauchy",
year = "1837",
title = "M\'emoire sur l'Interpolation",
journal = "Journal de Math\'ematiques Pures et Appliqu\'ees",
volume = "2",
pages = "193--205",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "la, interpolation, history"
}
-cb- -cc- -cd- -ce-
@article{ceel:82,
author = "Y. Censor and T. Elfving",
year = "1982",
title = "New Methods for Linear Inequalities",
journal = "BIT",
volume = "42",
pages = "199--211",
kwds = "nla, linear inequalities"
}
-cf- -cg- -ch-
@article{cham:71,
author = "J. M. Chambers",
year = "1971",
title = "Regression Updating",
journal = "Journal of the American Statistical Association",
volume = "66",
pages = "744--748",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, stat, lsq, regr, updating"
}
@unpublished{cham:72,
author = "J. M. Chambers",
year = "1972",
title = "Stabilizing Linear Regression against Observational Error
in Independent Variats",
note = "Manuscript, Bell Laboratories, Murray Hill, New Jersey.",
kwds = "stat, svd, regr"
}
@book{cham:77,
author = "J. M. Chambers",
year = "1977",
title = "Computational Methods for Data Analysts",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, stat, na"
}
@article{chfp:77,
author = "S. P. Chan and R. Feldman and B. N. Parlett",
year = "1977",
title = "Algorithm 517: {A} Program for Computing the Condition
Numbers of Matrix Eigenvalues Without Computing Eigenvectors",
journal = "ACM Transactions on Mathematical Software",
volume = "3",
pages = "186--203",
kwds = "nla, eig, pert, condition estimation, software,
nonsymmetric matrix"
}
@article{chle:79,
author = "T. F. Chan and J. G. Lewis",
year = "1979",
title = "Computing Standard Deviation: Accuracy",
journal = "Communications of the ACM",
volume = "22",
pages = "536-531",
kwds = "stat, na, standard deviation, updating"
}
@article{chan:82,
author = "T. F. Chan",
year = "1982",
title = "An Improved Algorithm for Calculating the Singular Value
Decomposition",
journal = "ACM Transactions on Mathematical
Software",
volume = "8",
pages = "72-83",
kwds = "nla, svd, software"
}
@article{chan:82a,
author = "T. F. Chan",
year = "1982",
title = "Algorithm 581: An Improved Algorithm for Computing the Singular
Value Decomposition",
journal = "ACM Transactions on Mathematical Software",
volume = "8",
pages = "84--88",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, software"
}
@techreport{chgl:82,
author = "T. F. Chan and G. H. Golub and R. J. Le Veque",
year = "1982",
title = "Algorithms for Computing the Sample Variance: Analysis and
Recommendations",
institution = "Department of Computer Science, Yale University",
number = "222",
kwds = "stat, na, variance, standard deviation"
}
@article{chke:82,
author = "T. F. Chan and H. B. Keller",
year = "1982",
title = "Arc-Length Continuation and Multi-Grid Techniques for
Nonlinear Elliptic Eigenvalue Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "3",
pages = "173--194",
kwds = "nlop, pde, continuation, elliptic pde"
}
@article{chjz:83,
author = "T. F. Chan and K. R. Jackson and B. Zhu",
year = "1983",
title = "Alternating Direction Incomplete Factorizations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "239--257",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning, incomplete factorization"
}
@article{chan:84,
author = "T. F. Chan",
year = "1984",
title = "Deflated Decomposition Solutions of Nearly Singular Systems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "21",
pages = "738--754",
note = "Cited in \cite{govl:89}.",
kwds = "nla, deflation, linear system, condition"
}
@article{chan:84a,
author = "T. F. Chan",
year = "1984",
title = "On the Existence and Computation of {LU}-Factorizations
with Small Pivots",
journal = "Mathematics of Computation",
volume = "42",
pages = "535--547",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, lud, rank determination"
}
@techreport{chre:84,
author = "T. F. Chan and D. C. Resaco",
year = "1984",
title = "On the Condition of Nearly Singular Matrices Under
Rank-1 Perturbations",
institution = "Department of Computer Science, Yale University",
type = "Research Report",
number = "YALEU/DCS/RR-335",
kwds = "la, eig, pert, condition"
}
@article{chan:85,
author = "T. F. Chan",
year = "1985",
title = "On the Existence and Computation of {LU} Factorizations with small
pivots",
journal = "Mathematics of Computation",
volume = "42",
pages = "535--548",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting"
}
@inproceedings{chan:86,
author = "T. F. Chan",
year = "1986",
title = "Alternative to the {SVD}: Rank Revealing {QR}-Factorizations",
booktitle = "Proceedings of SPIE---The International Society for
Optical Engineering, V.~696. Advanced Algorithms
and Architectures for Signal Processing",
pages = "31--38",
publisher = "SPIE",
address = "Bellingham, Washington",
kwds = "nla, qrd, condition estimation, rank determination"
}
@article{chan:87,
author = "T. F. Chan",
year = "1987",
title = "Rank Revealing {QR}~Factorizations",
journal = "Linear Algebra and Its Applications",
volume = "88/89",
pages = "67--82",
kwds = "nla, qrd, condition estimation, rank determination"
}
@article{chan:88,
author = "T. F. Chan",
year = "1988",
title = "An Optimal Circulant Preconditioner for {Toeplitz}
Systems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "766-771",
kwds = "nla, linear system, Toeplitz matrix, preconditioning,
circulant matrix"
}
@book{cgpw:89,
author = "T. F. Chan and R. Glowinski and J. Periaux
and O. Widlund, eds.",
title = "Second International Symposium on Domain Decomposition
Methods",
publisher = "SIAM Publications",
address = "Philadelphia",
year = "1989",
kwds = "book, na, domain decomposition, pde"
}
@techreport{chha:89,
author = "T. F. Chan and P. C. Hansen",
year = "1990",
title = "A Stable Extension of {Levinson's} Algorithm for
Indefinite Toeplitz Systems",
institution = "Computational and Applied Mathematics,
Department of Mathematics, University of
California, Los Angeles",
type = "CAM Report",
number = "89--20",
kwds = "nla, Toeplitz matrix, Levinson's algorithm, indefinite system"
}
@article{chha:90,
author = "T. F. Chan and P. C. Hansen",
year = "1990",
title = "Computing Truncated Singular Value Decomposition Least
Squares Solutions by Rank Revealing {QR}-Factorizations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "11",
pages = "519--530",
kwds = "nla, svd, lsq, rank determination"
}
@unpublished{chha:91,
author = "T. F. Chan and P. C. Hansen",
year = "1991",
title = "Low-Rank Revealing {QR}~Factorizations",
note = "Manuscript",
kwds = "nla, qrd, condition, rank determination"
}
@techreport{chha:91a,
author = "T. F. Chan and P. C. Hansen",
year = "1991",
title = "Low-Rank Revealing {QR}~Factorizations",
institution = "Department of Mathematics, University of
California, Los Angeles",
type = "CAM Report",
number = "91-08",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, qrd, pivoting, rank determination"
}
@article{chha:92,
author = "T. F. Chan and P. C. Hansen",
year = "1992",
title = "Some Applications of the Rank Revealing {QR}~Factorization",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "13",
pages = "727--741",
kwds = "nla, qrd, condition, rank determination"
}
@techreport{chip:91,
author = "S. Chandrasekaran and I. Ipsen",
year = "1991",
title = "On Rank-Revealing {QR} Factorizations",
institution = "Yale University, Department of Computer Science",
type = "Technical Report",
number = "YALEU/DCS/RR-880",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, rank determination"
}
@article{chsa:88,
author = "H. Y. Chang and M. Salama",
year = "1988",
title = "A Parallel {H}ouseholder Tridiagonalization Stratagem
Using Scattered Square Decomposition",
journal = "Parallel Computing",
volume = "6",
pages = "297--312",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, eig, tridiagonal matrix"
}
@article{chvd:87,
author = "J. P. Charlier and Van Dooren, P.",
year = "1987",
title = "On {K}ogbetliantz's {SVD} Algorithm in the Presence of Clusters",
journal = "Linear Algebra and its Applications",
volume = "95",
pages = "135--160",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Kogbetliantz's algorithm, Jacobi-like, svd"
}
@article{chvd:88,
author = "J. P. Charlier and M. Vangegin and Van Dooren, P.",
year = "1988",
title = "On Efficient Implementations of {Kogbetliantz's}
Algorithm for Computing the Singular
Value Decomposition",
journal = "Numerische Mathematik",
volume = "52",
pages = "270-300",
kwds = "nla, svd, Kogbetliantz's algorithm, Jacobi-like"
}
@unpublished{chvd:88a,
author = "J. P. Charlier and Van Dooren, P.",
year = "1988",
title = "A {Jacobi}-Like Algorithm for Computing the
Generalized {Schur} Form of a Regular Pencil",
note = "Phillips Research Laboratory, Belgium.",
kwds = "nla, prll, geig, Jacobi-like"
}
@article{chat:74,
author = "F. Chatelin-Laborde",
year = "1974",
title = "Perturbation d'une matrice hermitienne ou normale",
journal = "Numerische Mathematik",
volume = "17",
pages = "318--337",
kwds = "la, eig, pert, symmetric matrix, normal matrix"
}
@article{chat:76,
author = "F. Chatelin-Laborde",
year = "1976",
title = "Calcul num\'erique des \'el\'ements propres d'op\'eateurs
diff\'erentiels int\'egraux par it\'eration",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris, S\'erie A",
volume = "283",
pages = "363--365",
kwds = "nla, eig, functional analysis"
}
@article{chle:78,
author = "F. Chatelin and J. Lemordant",
year = "1978",
title = "Error Bounds in the Approximation of the Eigenvalues
of Differential and Integral Operators",
journal = "J. Math. Anal. Appl.",
volume = "22",
pages = "257--271",
note = "Cited in \cite{parl:80}.",
kwds = "la, eig, pert, functional analysis"
}
@article{chmi:82,
author = "F. Chatelin and W. L. Miranker",
year = "1982",
title = "Acceleration by Aggregation of Successive Approximation
Methods",
journal = "Linear Algebra and Its Applications",
volume = "43",
pages = "17--47",
kwds = "nla, aggregation"
}
@book{chat:83,
author = "F. Chatelin",
year = "1983",
title = "Spectral Approximation of Linear Operators",
publisher = "Academic Press",
address = "New York",
kwds = "book, la, eig, pert, functional analysis"
}
@proceedings{chat:84,
year = "1984",
author = "F. Chatelin",
title = "Iterative Aggregation/Disaggregation Methods",
booktitle = "Mathematical Computer Performance and Reliability",
publisher = "Elsevier Science Publishers",
editor = "G. Iazeolla and P. J. Courtois and A. Hordijk",
address = "New York",
pages = "199-207",
kwds = "nla, eig, aggregation, Markov chain, iter"
}
@article{chmi:84,
author = "F. Chatelin and W. L. Miranker",
year = "1984",
title = "Aggregation/Disaggregation for Eigenvalue Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "21",
pages = "567--582",
kwds = "nla, eig, aggregation"
}
@incollection{chbr:88,
author = "F. Chatelin and M. C. Brunet",
year = "1988",
title = "A Probabilistic Round-off Error Propagation Model.
Application to the Eigenvalue Problem",
booktitle = "Reliable Numerical Software",
editor = "Cox and Harrarling",
publisher = "Oxford University Press",
note = "To appear.",
kwds = "la, eig, stochastic analysis, rounding error"
}
@article{chat:88b,
author = "F. Chatelin",
year = "1988",
title = "Sur le taux de fiabilit\'e g\'en\'eral del la m\'ethode {CESTAC}",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris, S\'erie I",
volume = "307",
pages = "851--854",
kwds = "na, rounding error, stochastic analysis"
}
@techreport{chat:88,
author = "F. Chatelin",
year = "1988",
title = "Analyse Statistique de la Qualite Numerique
et Arithmetic de la Resolution Approchee D'Equations
par Calcul Sur Ordinateur",
institution = "Centre Scientifique de Paris",
type = "Etude",
number = "F.133",
kwds = "la, pert, rounding error"
}
@article{chat:88a,
author = "F. Chatelin",
year = "1988",
title = "De l'utilisation en calcul matriciel de mod\`eles
probabilistes pour la simulation des erreurs de calcul",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris, S\'erie I",
volume = "307",
pages = "847--850",
kwds = "nla, pert, rounding error"
}
@inproceedings{chbr:90,
author = "F. Chatelin and M. C. Brunet",
year = "1990",
title = "A Probabilistic Round-off Error Propagation Model.
{Application} to the Eigenvalue Problem",
booktitle = "Reliable Numerical Software",
editor = "D. Cox and S. Hammarling",
pages = "139--160",
publisher = "Clarendon Press",
address = "Oxford",
kwds = "na, nla, pert, rounding error, stochastic analysis"
}
@article{cheb:1859,
author = "P. L. Chebyshev",
year = "1859",
title = "Sur l'interpolation par la methode des moindres
carr\'es",
journal = "M\'emoires de l'Academie Imp\'eriale des
sciences de St.-Petersbourg, VII\,$^e$ s\'erie",
volume = "15",
pages = "1-24",
kwds = "la, nla, Gram-Schmidt algorithm, interpolation, polynomial,
history"
}
@article{chks:78,
author = "S. Chen and D. Kuck and A. Sameh",
year = "1978",
title = "Practical Parallel Band Triangular Systems Solvers",
journal = "{ACM} Transactions on Mathematical Software",
volume = "4",
pages = "270--277",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, tridiagonal matrix, linear system"
}
@article{chdh:84,
author = "S. Chen and J. Dongarra and C. Hsuing",
title = "Multiprocessing Linear Algebra Algorithms on the {Cray X-MP-2}:
Experiences with Small Granularity",
year = "1984",
journal = "Journal of Parallel and Distributed ",
volume = "1",
pages = "22--31",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll"
}
@article{chte:72,
author = "Y.T. Chen and R.P. Tewarson",
year = "1972",
title = "On the Fill-in when Sparse Vectors are Orthonormalized",
journal = "Computing",
volume = "9",
pages = "53--56",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, orthogonalization"
}
@article{chsa:87,
author = "K. H. Cheng and S. Sahni",
year = "1987",
title = "{VLSI} Systems for Band Matrix Multiplication",
journal = "Parallel ",
volume = "4",
pages = "239--258",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, matrix multiplication"
}
@article{chmd:84,
author = "R. C. Chin and T. A. Manteuffel and de Pillis, J.",
year = "1984",
title = "{ADI} as a Preconditioning for Solving the Convection-Diffusion
Equation",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "5",
pages = "281--299",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning"
}
@inproceedings{chzp:88,
author = "L Chisci and G. Zappa",
year = "1988",
title = "High Throughput Parallel Implementation of RLS",
booktitle = "Identification and Systm Parameter Estimatin, 1988",
editor = "H.-F. Chen",
pages = "561--566",
publisher = "Pergamon Press",
address = "Oxford",
kwds = "nla, systolic, lsq, updating"
}
@article{chht:68,
author = "R. Choudary and Hanumara and W. A. Thompson Jr.",
year = "1968",
title = "Percentage Points of the Extreme Roots of a {Wishart} Matrix",
journal = "Biometrika",
volume = "55",
pages = "505-512",
kwds = "stat, Wishart matrix, distribution"
}
@article{chhm:90,
author = "M. L. Chaudhry and C. M. Harris and W. G. Marchal",
year = "1990",
title = "Robustness of Rootfinding in Single-Server Queueing Models",
journal = "ORSA Journal on Computing",
volume = "2",
pages = "273--286",
kwds = "nlop, queue, polynomial, Markov chain"
}
@article{chkl:87,
author = "J. Chun and T. Kailath and H. L. Ari",
year = "1987",
title = "Fast Parallel Algorithms for {QR}~and Triangular
Factorization",
journal = "SIAM Journal on Parallel and Scientific Compting",
volume = "8",
pages = "899-913",
kwds = "nla, prll, qrd, lud, fast algorithm"
}
@article{chu:86,
author = "M. Chu",
year = "1986",
title = "A Differential Equation Approach to the Singular Value
Decomposition of Bidiagonal Matrices",
journal = "Linear Algebra and Its Applications",
volume = "80",
pages = "71--79",
kwds = "nla, svd, bidiagonal matrix, flow algorithm"
}
@phdthesis{chun:89,
author = "J. Chun",
year = "1989",
title = "Fast Array Algorithms for Structured Matrices",
school = "Department of Electrical Engineering, Stanford University",
kwds = "nla, fast algorithm, Toeplitz matrix, Vandermonde matrix,
Hankel matrix"
}
-ci-
@article{cimm:39,
author = "G. Cimmino",
year = "1939",
title = "Calcolo approssimato per le soluzioni dei sistemi di equazioni
lineari",
journal = "Ric. Sci. Progr. tecn. econom. naz.",
volume = "9",
pages = "326--333",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, projection method"
}
-cj- -ck- -cl-
@article{clos:88,
author = "D. I. Clark and M. R. Osborne",
year = "1988",
title = "On Linear Restricted and Interval Least-squares Problems",
journal = "IMA Journal on Numerical Analysis",
volume = "8",
pages = "23--36",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, rounding error, constraints"
}
@article{clol:84,
author = "C. W. Clenshaw and F. W. J. Olver",
year = "1984",
title = "Beyond Floating Point",
journal = "Journal of the ACM",
volume = "31",
pages = "319--328",
note = "Cited in \cite{demm:87b}.",
kwds = "rounding error, computer arithmetic"
}
@article{clin:73,
author = "A. K. Cline",
year = "1973",
title = "An Elimination Method for the Solution of Linear Least
squares problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "283--289",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, lud, normal equations"
}
@article{clin:76,
author = "A. K. Cline",
year = "1976",
title = "A Descent Method for the Uniform Solution to Overdetermined
Systems of Equations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "13",
pages = "293--309",
note = "Cited in \cite{govl:89}.",
kwds = "nla, l1 approximation, overdetermined system"
}
@techreport{clin:76a,
author = "A. K. Cline",
year = "1976",
title = "Several observations on the Use of Conjugate Gradient Methods",
type = "report",
number = "76-22",
institution = "ICASE, NASA Langley Research Center",
address = "Hampton, VA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients"
}
@incollection{clgp:76,
author = "A. K. Cline and G. H. Golub and G. W. Platzman",
year = "1976",
title = "Calculation of Normal Modes of Oceans Using a {L}anczos Method",
booktitle = "Sparse Matrix Computations",
editor = "J. R. Bunch and D. J. Rose",
publisher = "Academic Press",
address = "New York",
pages = "409--426",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm"
}
@article{cmsw:79,
author = "A. K. Cline and C. B. Moler and G. W. Stewart
and J. H. Wilkinson",
year = "1979",
title = "An Estimate for the Condition Number of a Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "16",
pages = "368-375",
kwds = "math, nla, condition estimation"
}
@unpublished{clin:??,
author = "A. K. Cline",
year = "19??",
title = "A Counter Example to the Condition Number
Estimator Found in ``An Estimate of the Condition Number
of a Matrix''",
note = "Handwritten manuscript, Department of Computer Science
University of Texas, Austin",
kwds = "nla, lud, condition estimation"
}
@incollection{clcv:82,
author = "A. K. Cline and A. R. Conn and C. F. {Van Loan}",
year = "1982",
title = "Generalizing the {LINPACK} Condition Estimator",
editor = "J.P. Hennart",
booktitle = "Numerical Analysis",
publisher = "Springer Verlag",
series = "Lecture Notes in Mathematics No. 909",
address = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition estimation, rounding error"
}
@article{clin:83,
author = "A. K. Cline and R. K. Rew",
year = "1983",
title = "A Set of Counter examples to Three Condition Number Estimators",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "4",
pages = "602--611",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition estimation"
}
@article{clpl:76,
author = "R. E. Cline and R. J. Plemmons",
year = "1976",
title = "$\ell_2$-solutions to Underdetermined Linear Systems",
journal = "SIAM Review",
volume = "18",
pages = "92--106",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, underdetermined system, l1 approximation"
}
@article{clje:70,
author = "M. Clint and A. Jennings",
year = "1970",
title = "The Evaluation of Eigenvalues and Eigenvectors of
Real Symmetric Matrices by Simultaneous Iteration",
journal = "Computer Journal",
volume = "13",
pages = "76--80",
kwds = "nla, eig, subspace iteration, symmetric matrix, sparse"
}
@article{clje:71,
author = "M. Clint and A. Jennings",
year = "1971",
title = "A Simultaneous Iteration Method for the Unsymmetric
Eigenvalue Problem",
journal = "Journal of the Institute for Mathematics and Applications",
volume = "8",
pages = "111--121",
kwds = "nla, eig, subspace iteration, nonsymmetric matrix, sparse"
}
-cl- -cm- -cn- -co-
@article{coch:38,
author = "W. G. Cochran",
year = "1938",
title = "The Omission or Addition of an Independent Variate in Multiple
Linear Regression",
journal = "Suppl. Journ. Roy. Stat. Soc.",
volume = "5",
pages = "171-176",
kwds = "stat, regr, updating"
}
@article{coch:68,
author = "W. G. Cochran",
year = "1968",
title = "Errors of Measurement in Statistics",
journal = "Technometrics",
volume = "10",
pages = "637-666",
kwds = "stat, measurement error"
}
@article{cohe:72,
author = "A. F. Cohen",
year = "1972",
title = "Rate of Convergence of Several Conjugate Gradient
Algorithms",
journal = "SIAM Journal on Numerical Analysis",
volume = "9",
pages = "248--259",
kwds = "nla, conjugate gradients"
}
@article{cohe:74,
author = "A. M. Cohen",
year = "1974",
title = "A Note on Pivot Size in {G}aussian Elimination",
journal = "Linear Algebra and its Applications",
volume = "8",
pages = "361--368",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting"
}
@article{cohn:22,
author = "A. Cohn",
year = "1922",
title = " {\"Uber die Anzal der Wurzeln einer algebraischen
Gleichung in einem Kreise}",
journal = "Math. Z.",
volume = "14",
pages = "112--148",
kwds = "nlop, polynomial"
}
@techreport{coso:82,
author = "Thomas F. Coleman and Danny C. Sorensen",
year = "1982",
title = "A Note on the Computation of an Orthonormal Basis
for the Null Space of a Matrix",
institution = "Department of Computer Science, Cornell University",
type = "Technical Report",
number = "TR 82-510",
kwds = "nla, nlop, null space"
}
@book{covl:88,
author = "T. Coleman and Van Loan, C.",
year = "1988",
title = "Handbook for Matrix Computations",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla"
}
@article{coll:48,
author = "A. R. Collar",
year = "1948",
title = "Some Notes on {Jahn}'s Method for the Improvement of Approximate
Laten Roots and Vectors of a Square Matrix",
journal = "Quarterly Journal of Mechanics and Applied Mathematics",
volume = "1",
pages = "145--148",
kwds = "nla, eig"
}
@article{coeg:86,
author = "T. F. Coleman and A. Edenbrandt and J. R. Gilbert",
year = "1986",
title = "Predicting Fill for Sparse Orthogonal Factorization",
journal = "Journal of the ACM",
volume = "33",
pages = "517--532",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, sparse"
}
@article{cogo:90,
author = "P. Comon and G. H. Golub",
year = "1990",
title = "Tracking a Few Extreme Singular Values and Vectors
in Signal Processing",
journal = "Proc. IEEE",
volume = "78",
pages = "1327--1343",
kwds = "nla, signal processing, Lanczos algorithm, rank determination"
}
@article{cogo:73,
author = "P. Concus and G. H. Golub",
year = "1973",
title = "Use of Fast Direct Methods for the Efficient Numerical Solution of
Nonseparable Elliptic Equations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "10",
pages = "1103--1120",
note = "Cited in \cite{govl:89}.",
kwds = "nla, fast algorithm, elliptic pde, direct Poisson solver"
}
@incollection{cogo:76,
author = "P. Concus and G. H. Golub and D. P. O'Leary",
year = "1976",
title = "A Generalized Conjugate Gradient Method for the Numerical Solution
of Elliptic Partial Differential Equations",
booktitle = "Sparse Matrix Computations",
editor = "J. R. Bunch and D. J. Rose",
publisher = "Academic Press",
address = "New York, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, elliptic pde"
}
@article{cogm:85,
author = "P. Concus and G. H. Golub and G. Meurant",
year = "1985",
title = "Block Preconditioning for the Conjugate Gradient Method",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "6",
pages = "220--252",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, preconditioning, conjugate gradients"
}
@book{codb:80,
author = "S. D. Conte and de Boor, C.",
year = "1980",
title = "Elementary Numerical Analysis: An Algorithmic Approach",
publisher = "McGraw-Hill",
address = "New York, NY",
edition = "third",
note = "Cited in \cite{govl:89}.",
kwds = "book, na"
}
@article{cook:79,
author = "R. D. Cook",
year = "1979",
title = "Influential Observations in Linear Regression",
journal = "Journal of American Statistic Association",
volume = "74",
pages = "169-174",
kwds = "stat, regr, influence, diagnostic"
}
@article{cowe:80,
author = "R. D. Cook and S. Weisberg",
year = "1980",
title = "Characterization of an Empirical Influence Function for Detecting
Influential Cases in Regression",
journal = "Technometrics",
volume = "22",
pages = "495-508",
kwds = "stat, regr, influence, diagnostic"
}
@book{cowe:82,
author = "R. D. Cook and S. Weisberg",
year = "1982",
title = "Residuals and Influence in Regression",
publisher = "Chapman--Hall",
address = "New York",
kwds = "book, stat, regr, influence, diagnostic"
}
@article{coop:48,
author = "J. L. B. Cooper",
year = "1948",
title = "The Solution of Natural Frequence Equations by
Relaxation Methods",
journal = "Quarterly for Applied Matheamtics",
volume = "6",
pages = "179--183",
kwds = "nla, geig, relaxation, symmetric matrix, sparse"
}
@article{coru:79,
author = "J. E. Cope and B. W. Rust",
year = "1979",
title = "Bounds on Solutions of Systems with Inaccurate Data",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "16",
pages = "950--963",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pert, linear system, confidence interval"
}
@mastersthesis{corn:65,
author = "D. Corneil",
year = "1965",
title = "Eigenvalues and Orthogonal Eigenvectors of Real
Symmetric Matrices",
school = "Department of Computer Science, University of Toronto",
kwds = "nla, eig, symmetric matrix"
}
@article{comr:86,
author = "M. Costnard and J. M. Muller and Y. Robert",
year = "1986",
title = "Parallel {QR} Decomposition of a Rectangular Matrix",
journal = "Numerische Mathematik",
volume = "48",
pages = "239--250",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, prll"
}
@article{comr:88,
author = "M. Costnard and M. Marrakchi and Y. Robert",
year = "1988",
title = "Parallel {G}aussian Elimination on an {MIMD} Computer",
journal = "Parallel Computing",
volume = "6",
pages = "275--296",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, prll, mimd"
}
@inproceedings{coda:89,
author = "M. Costnard and E. M. Daoudi",
year = "1989",
title = "{Householder} Factorization on Distributed
Architectures",
booktitle = "International Meeting on Parallel Computing,
Verona, Italy, 1988",
editor = "",
pages = "91--102",
publisher = "IOP Publishing Ltd.",
address = "",
kwds = "nla, Householder transformation, prll"
}
@article{cott:74,
author = "R. W. Cottle",
year = "1974",
title = "Manifestations of the {Schur} Complement",
journal = "Linear Algebra and Its Applications",
volume = "8",
pages = "189--211",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "la, Schur complement"
}
@article{cott:75,
author = "I. W. Cotton",
year = "1975",
title = "Remark on Stably Updating Mean and Standard Deviation
of Data",
journal = "Communications of the ACM",
volume = "19",
pages = "458",
kwds = "stat, updating, mean, standard deviation, variance"
}
@article{cour:20,
author = "R. Courant",
year = "1920",
title = " {Ueber die Eigenwert bei den Differentialgleichungen
der Mathematischen Physik}",
journal = "Mathematische Zeitschrift",
volume = "7",
pages = "1--57",
kwds = "la, eig, pert, ode, pde"
}
@book{cohi:53,
author = "R. Courant and D. Hilbert",
year = "1953",
title = "Methods of Mathematical Physics V.I",
publisher = "Interscience Publishers",
address = "New York",
kwds = "book, math, physics"
}
@article{cour:75,
author = "P.-J. Courtois",
year = "1975",
title = "Error Analysis in Nearly-Completely Decomposable Stochastic
Systems",
journal = "Econometrica",
volume = "43",
pages = "691--709",
kwds = "la, nla, Markov chain, nearly uncoupled system"
}
@article{cova:76,
author = "P.-J. Courtois and H. Vantilborgh",
year = "1976",
title = "A Decomposable Model of Program Paging Behavior",
journal = "Acta Informatica",
volume = "6",
pages = "251--275",
kwds = "memory hierarchy, Markov chain, nearly uncoupled system"
}
@book{cour:77,
author = "P.-J. Courtois",
year = "1977",
title = "Decomposability",
publisher = "Academic Press",
address = "New York",
kwds = "book, nla, nearly uncoupled system, Markov chain, aggregation"
}
@inproceedings{cour:82,
author = "P.-J. Courtois",
year = "1982",
title = "Error Minimization in Decomposable Stochastic Models",
booktitle = "Applied Probability--Computer Science: The Interface,
Volume I",
editor = "R. L. Disney and T. J. Ott",
pages = "189--210",
publisher = "Birkh{\"a}user",
address = "Boston",
kwds = "nla, Markov chain, eig, nearly uncoupled system, aggregation"
}
@inproceedings{cose:84,
author = "P. J. Courtois and P. Semal",
year = "1984",
title = "Error Bounds for the Analysis by Decomposition of
Non-Negative Matrices",
booktitle = "Mathematical Computer Performance and Reliability",
editor = "G. Iazeolla and P. J. Courtois and A. Hordijk",
pages = "287-302",
publisher = "Elsevier",
address = "Amsterdam",
kwds = "la, nearly uncoupled system, Markov chain, aggregation"
}
@article{cose:86,
author = "P.-J. Courtois and P. Semel",
year = "1986",
title = "Block Iterative Algorithms for Stochastic Matrices",
journal = "Linear Algebra and Its Applications",
volume = "76",
pages = "59--70",
kwds = "nla, Markov chain, iter"
}
@article{coda:82,
author = "M. Cowles and C. Davis",
year = "1982",
title = "On the Origins of the .05 Level of Statistical Significance",
journal = "American Psychologist",
volume = "37",
pages = "553--558",
kwds = "stat, history, hypothesis testing"
}
@article{cox:81,
author = "M. G. Cox",
year = "1981",
title = "The Least Squares Solution of Overdetermined Linear Equations
having Band or Augmented Band Structure",
journal = "IMA Journal on Numerical Analysis",
volume = "",
pages = "3--22",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, band matrix"
}
@incollection{cox:90,
author = "M. G. Cox",
year = "1990",
title = "The Least-squares Solution of Linear Equations with Block-angular
Observation Matrix",
pages = "227--240",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. J. Hammarling",
publisher = "Oxford University Press",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
-cp- -cq- -cr-
@article{cran:51,
author = "S. H. Crandall",
year = "1951",
title = " On a Relaxation Procedure for Eigenvalue Problems",
journal = "J. Math. Phys.",
volume = "39",
pages = "416--423",
kwds = "nla, geig, iter, relaxation, sparse"
}
@article{cran:51a,
author = "S. H. Crandall",
year = "1951",
title = "Iterative Procedures Related to Relaxation Methods
for Eigenvalue Problems",
journal = "J. Math. Phys.",
volume = "39",
pages = "416--423",
kwds = "nla, geig, iter, relaxation"
}
@article{crwa:79,
author = "P. Craven and G. Wahba",
year = "1979",
title = "Smoothing Noisy Data with Spline Functions",
journal = "Numerische Mathematik",
volume = "31",
pages = "377--403",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "na, spline, smoothing"
}
@phdthesis{craw:70,
author = "C. R. Crawford",
year = "1970",
title = "The Numerical Solution of the Generalized Eigenvalue
Problem",
school = "Department of Mathematics, University of Michigan",
kwds = "nla, geig, symmetric matrix"
}
@article{craw:73,
author = "C. R. Crawford",
year = "1973",
title = "Reduction of a Band-Symmetric Generalized Eigenvalue
Problem",
journal = "Communications of the ACM",
volume = "16",
pages = "41--44",
kwds = "nla, geig, band matrix, symmetric matrix"
}
@article{craw:76,
author = "C. R. Crawford",
year = "1976",
title = "A Stable Generalized Eigenvalue Problem",
journal = "SIAM Journal on Numerical Analysis",
volume = "13",
pages = "854--860",
kwds = "la, geig, pert, symmetric matrix"
}
@article{crmo:83,
author = "C. R. Crawford and Y. S. Moon",
year = "1983",
title = "Finding a Positive Definite Linear Combination of Two {H}ermitian
Matrices",
journal = "Linear Algebra and its Applications",
volume = "51",
pages = "37--48",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, symmetric matrix"
}
@techreport{craw:83,
author = "C. R. Crawford",
year = "1983",
title = "A Routine to Find a Positive Definite Linear Combination
of two Real Symmetric Matrices",
institution = "Department of Computer Science, York University",
type = "Technical Report",
number = "83-02",
kwds = "nla, geig, symmetric matrix"
}
@techreport{craw:83a,
author = "C. R. Crawford",
year = "1983",
title = "On the Convergence of a Matrix Algorithm",
institution = "Department of Computer Science, York University",
type = "Technical Report",
number = "83-06",
kwds = "nla, geig, symmetric matrix"
}
@article{craw:86,
author = "C. R. Crawford",
year = "1986",
title = "Algorithm~646 {PDFIND}: A Routine to Find a
Positive Definite Linear Combination of Two Real
Symmetric Matrices",
journal = "{ACM} Transactions on Mathematical Software",
volume = "12",
pages = "278--282",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, symmetric matrix"
}
@techreport{crou:41,
author = "P. D. Crout",
year = "1941",
title = "A Short Method for Evaluating Determinants and Solving
Systems of Linear Equations",
institution = "Marchant Calculating Machine Co.",
type = "Marchant Methods",
number = "MM-182",
note = "Cited in \cite{dwye:51}.",
kwds = "nla, Crout's method, lud, determinant"
}
@inproceedings{crst:91,
author = "J. J. Cruz and S. Stidham",
year = "1991",
title = "Iterative Methods for Determining Derivatives
of Stationary Distributions for Finite {Markov}
Chains",
booktitle = "Numerical Solution of {Markov} Chains",
editor = "W. J. Stewart",
pages = "121--130",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, queue"
}
@article{crye:68,
author = "C. W. Cryer",
year = "1968",
title = "Pivot Size in {Gaussian} Elimination",
journal = "Numerische Mathematik",
volume = "12",
pages = "335--345",
kwds = "nla, pivoting, rounding error"
}
-cs- -ct- -cu-
@inproceedings{cudo:74,
author = "J. Cullum and W. E. Donath",
year = "1974",
title = "A Block {L}anczos Algorithm for Computing the {Q} Algebraically
Largest Eigenvalues and a Corresponding Eigenspace of Large,
Sparse Real Symmetric Matrices",
booktitle = "Proceedings of the 1974 IEEE Conference on Decision and
Control, {Phoenix, AZ}",
pages = "505--509",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm, sparse, block algorithm"
}
@techreport{cuwi:77,
author = "J. Cullum and R. A. Willoughby",
year = "1977",
title = "The Equivalence of the {L}anczos and the Conjugate Gradient
Algorithms",
number = "RC-6903",
institution = "IBM",
address = "Yorktown Heights, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, conjugate gradients, Lanczos algorithm"
}
@article{cull:78,
author = "J. Cullum",
year = "1978",
title = "The Simultaneous Computation of a Few of the Algebraically Largest
and Smallest Eigenvalues of a Large Sparse Symmetric Matrix",
journal = "{BIT}",
volume = "18",
pages = "265--275",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, sparse"
}
@inproceedings{cuwi:79,
author = "J. Cullum and R. A. Willoughby",
year = "1979",
title = "{L}anczos and the Computation in Specified Intervals of the
Spectrum of Large, Sparse Real Symmetric Matrices",
booktitle = "Sparse Matrix Proceedings 1978",
editor = "I. S. Duff and G. W. Stewart",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm"
}
@article{cuwi:80,
author = "J. Cullum and R. A. Willoughby",
year = "1980",
title = "The {L}anczos Phenomena: An Interpretation Based on Conjugate
Gradient Optimization",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "63--90",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm, conjugate gradients"
}
@article{cuwi:81,
author = "J. Cullum and R. A. Willoughby",
year = "1984",
title = "Computing Eigenvalues of Very Large Symmetric
Matrices\,---\,An Implementiion of a {Lanczos} Algorithm with
No Reorthogonalization",
journal = "Journal of Computational Physics",
volume = "44",
pages = "329--358",
kwds = "nla, eig, sparse, Lanczos algorithm, symmetric matrix"
}
@article{cuwl:83,
author = "J. Cullum and R. A. Willoughby and M. Lake",
year = "1983",
title = "A {Lanczos} Algorithm for Computing Singular Values and
Vectors of Large Matrices",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "4",
pages = "197--215",
kwds = "nla, svd, sparse, Lanczos algorithm"
}
@book{cuwi:85,
author = "J.K. Cullum and R.A. Willoughby",
year = "1985",
title = "Lanczos Algorithms for Large Symmetric Eigenvalue Computations",
volume = "1 Theory. 2 Programs",
publisher = "Birkh{\"a}user",
address = "Stuttgart",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, eig, sparse, lanczos algorithm"
}
@book{cuwi:86,
editor = "J. Cullum and R. A. Willoughby",
year = "1986",
title = "Large Scale Eigenvalue Problems",
publisher = "North-Holland",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, eig, sparse"
}
@article{cupp:81,
author = "J. J. M. Cuppen",
year = "1981",
title = "A Divide and Conquer Method for the Symmetric Eigenproblem",
journal = "Numerische Mathematik",
volume = "36",
pages = "177--195",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, prll, symmetric matrix, tridiagonal matrix"
}
@article{cupp:83,
author = "J. J. M. Cuppen",
year = "1983",
title = "The Singular Value Decomposition in Product Form",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "4",
pages = "216--222",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, updating"
}
@article{cupp:84,
author = "J. J. M. Cuppen",
year = "1984",
title = "On Updating Triangular Products of {H}ouseholder Matrices",
journal = "Numerische Mathematik",
volume = "45",
pages = "403--410",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Householder transformation, updating"
}
@article{cure:71,
author = "A. R. Curtis and J. K. Reid",
year = "1971",
title = "The Solution of Large Sparse Unsymmetric Systems of
Linear Equations",
journal = "Journal of the Institute for Mathematics and Its Applications",
volume = "8",
pages = "344--353",
kwds = "nla, lud, linear system, sparse, nonsymmetric matrix"
}
@article{cure:72,
author = "A. R. Curtis and J. K. Reid",
year = "1972",
title = "On the Automatic Scaling of Matrices for {Gaussian}
Elimination",
journal = "Journal of the Institute for Mathematics and Applications",
volume = "10",
pages = "118--124",
kwds = "nla, lud, scaling"
}
@inproceedings{cuth:72,
author = "E. Cuthill",
year = "1972",
title = "Several Strategies for Reducing the Bandwidth of Matrices",
booktitle = "Sparse Matrices and Their Applications",
editor = "D. J. Rose and R. A. Willoughby",
pages = "157--166",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, sparse, band matrix"
}
-cv- -cw- -cx- -cy-
@phdthesis{cybe:78,
author = "G. Cybenko",
year = "1978",
title = "Error Analysis of Some Signal Processing Algorithms",
school = "Princeton University",
address = "Princeton, NJ",
note = "Cited in \cite{govl:89}.",
kwds = "nla, signal processing"
}
@article{cybe:80,
author = "G. Cybenko",
year = "1980",
title = "The Numerical Stability of the {L}evinson-{D}urbin Algorithm for
{T}oeplitz Systems of Equations",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "1",
pages = "303--310",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, fast algorithm, Levinson's algorithm,
Toeplitz matrix"
}
@article{cybe:84,
author = "G. Cybenko",
year = "1984",
title = "The Numerical Stability of the Lattice Algorithm for Least
Squares Linear Prediction Problems",
journal = "BIT",
volume = "24",
pages = "441--455",
kwds = "nla, toeplitz matrix, fast algorithm, rounding error"
}
@article{cyvl:86,
author = "G. Cybenko and Van Loan, C.",
year = "1986",
title = "Computing the Minimum Eigenvalue of a Symmetric Positive Definite
{T}oeplitz Matrix",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "7",
pages = "123--131",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Toeplitz matrix"
}
@article{cybe:89,
author = "G. Cybenko",
year = "1989",
title = "Dynamic Load Balancing for Distributed Memory
Multiprocessors",
journal = "Journal of Parallel and Distributed Computing",
volume = "7",
pages = "279--301",
kwds = "prll, distributed memory, load balancing"
}
-cz-
-da-
@book{dawo:71,
author = "C. Daniel and F. S. Wood",
year = "1971",
title = "Fitting Equations to Data",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr, lsq"
}
@book{dawo:80,
author = "C. Daniel and F. S. Wood",
year = "1980",
title = "Fitting Equations to Data",
edition = "second",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr, lsq"
}
@article{dani:67,
author = "J. W. Daniel",
year = "1967",
title = "The Conjugate Gradient Method for Linear and
Nonlinear Operator Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "4",
pages = "10--26",
kwds = "nla, nlop, conjugate gradients, linear system"
}
@article{dani:67a,
author = "J. W. Daniel",
year = "1967",
title = "Convergence of the Conjugate Gradient Method with
Computationally Convenient Modifications",
journal = "Numerische Mathematik",
volume = "10",
pages = "125--131",
kwds = "nla, nlop, conjugate gradients"
}
@article{dgks:76,
author = "J. Daniel and W. B. Gragg and L. Kaufman and G. W. Stewart",
year = "1976",
title = "Reorthogonalization and Stable Algorithms for Updating the
{Gram--Schmidt} {QR}~Factorization",
journal = "Mathematics of Computation",
volume = "30",
pages = "772-795",
kwds = "nla, qrd, updating, Gram-Schmidt algorithm"
}
@book{dant:63,
author = "G. B. Dantzig",
year = "1963",
title = "Linear Programming and Extensions",
publisher = "Princeton University Press",
address = "Princeton, New Jersey",
kwds = "book, nla, nlop, linear programming"
}
@article{dara:72,
author = "J. N. Darroch and D. Ratcliff",
year = "1972",
title = "Generalized Iterative Scaling for Log-Linear Models",
journal = "Annals of Mathematical Statistics",
volume = "43",
pages = "1470--1480",
kwds = "stat, log-linear model"
}
@book{djkp:88,
author = "B. N. Datta and C. R. Johnson and M. A. Kaashoek
and R. Plemmons and E. D. Sontag",
year = "1988",
title = "Linear Algebra in Signals, Systems, and Control",
publisher = "{SIAM} Publications",
address = "Philadelphia",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, signal processing, control"
}
@article{daub:90,
author = "I. Daubechies",
year = "1990",
title = "The Wavelet Transform, Time-Frequency Localization
and Signal Analysis",
journal = "IEEE Transactions on Information Theory",
volume = "36",
pages = "961--1005",
kwds = "math, wavelet"
}
@article{daug:67,
author = "V. A. Daugavet",
year = "1967",
title = "Variant of the Stepped Exponential Method of
Finding Some of the First Characteristic Values
of a Symmetric Matrix",
journal = "USSR Comp. Math. and Math. Phys.",
volume = "8",
pages = "212--223",
note = "Original in Russian in {\it Zh. bychisl. Mat. mat. Fiz.\/}
{\bf 8} (1968) 158--165.",
kwds = "nla, eig, sparse, subspace iteration, symmetric matrix"
}
@techreport{dast:88,
author = "Nancy David and G. W. Stewart",
year = "1988",
title = "Hypothesis Testing with Errors in the Variables",
institution = "University of Maryland Department of Computer
Science",
type = "Technical Report",
number = "TR-1735",
kwds = "regr, eriv, pert, hypothesis testing"
}
@techreport{davi:59,
author = "W. C. Davidon",
year = "1959",
title = "Variable Metric Method for Minimization",
institution = "Argonne National Laboratory",
type = "AEC Research and Development Report",
number = "ANL-5990",
kwds = "nlop, quasi-Newton, Davidon's method"
}
@article{davi:75,
author = "E. R. Davidson",
year = "1975",
title = "The Iterative Calculation of A Few of the Lowest
Eigenvalues and Corresponding Eigenvectors of
Large Real-Symmetric Matrices",
journal = "Journal of Computational Physics",
volume = "17",
pages = "87--94",
kwds = "nla, eig, sparse, symmetric matrix"
}
@article{dahu:75,
author = "R. B. Davies and B. Hutton",
year = "1975",
title = "The Effects of Errors in the Independent Variables in Linear
Regression",
journal = "Biometrika",
volume = "62",
pages = "383-391",
kwds = "stat, regr, eriv, pert"
}
@article{davi:58,
author = "C. Davis",
year = "1958",
title = "Separation of Two Linear Subspaces",
journal = "Acta Scientiarum Mathematicarum",
volume = "19",
pages = "172--187",
kwds = "la, norm, canonical angles, subspace metric"
}
@article{davi:63,
author = "C. Davis",
year = "1963",
title = "The Rotation of Eigenvectors by a Perturbation",
journal = "Journal of Mathematical Analysis and Applications",
volume = "6",
pages = "159--173",
kwds = "la, eig, pert, symmetric matrix"
}
@article{davi:65,
author = "C. Davis",
year = "1965",
title = "The Rotation of Eigenvectors by a Perturbation.~{II}",
journal = "Journal of Mathematical Analysis and Applications",
volume = "11",
pages = "20--27",
kwds = "la, eig, pert, symmetric matrix"
}
@article{daka:70,
author = "C. Davis and W. Kahan",
year = "1970",
title = "The Rotation of Eigenvectors by a Perturbation.~{III}",
journal = "SIAM Journal on Numerical Analysis",
volume = "7",
pages = "1-46",
kwds = "math, la, nla, pert, eig, invariant subspace, symmetric matrix"
}
@article{davi:71,
author = "C. Davis",
year = "1974",
title = "The {Toeplitz-Hausdorff} Theorem Explained",
journal = "Canadian Mathematical Bulletin",
volume = "14",
pages = "245--246",
kwds = "la, field of values, eig"
}
@article{davi:73,
author = "C. Davis",
year = "1973",
title = "Explicit Functional Calculus",
journal = "Linear Algebra and Its Applications",
volume = "6",
pages = "193--199",
kwds = "la, eig, matrix function"
}
@article{dakw:82,
author = "C. Davis and W. Kahan and H. Weinberger",
year = "1982",
title = "Norm-Preserving Dilations and Their Applications to
Optimal Error Bounds",
journal = "SIAM Journal on Numerical Analysis",
volume = "19",
pages = "445--469",
kwds = "la, nla, pert, eig, dilation, symmetric matrix"
}
@article{davi:86,
author = "G. J. Davis",
year = "1986",
title = "Column {LU} Pivoting on a Hypercube Multiprocessor",
journal = "{SIAM} Journal on Algebraic and Discrete Methods",
volume = "7",
pages = "538--550",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, lud, pivoting, hypercube"
}
@article{daka:77,
author = "A. Dax and S. Kaniel",
year = "1977",
title = "Pivoting Techniques for Symmetric {G}aussian Elimination",
journal = "Numerische Mathematik",
volume = "28",
pages = "221--242",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting, symmetric matrix"
}
@article{dax:83,
author = "A. Dax",
year = "1983",
title = "A Diagonal Modification for the Downdating Algorithm",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "4",
pages = "85--93",
kwds = "nla, updating"
}
@article{daxa:89,
author = "A. Dax",
year = "1989",
title = "The $\ell_1$ Solution of Linear Equations Subject to Linear
Constraints",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "10",
pages = "328--340",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, l1 approximation, constraints"
}
@article{dape:88,
author = "J. Day and B. Peterson",
year = "1988",
title = "Growth in {G}aussian Elimination",
journal = "American Mathematical Monthly",
volume = "95",
pages = "489--513",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting"
}
@techreport{dadu:90,
author = "M. J. Dayd\'e and I. S. Duff",
year = "1990",
title = "Use of Level 3 {BLAS} in {LU}~Factorization
in a Multiprocessing Environment on Three Vector
Mulitprocessors: the {ALLIANT FX/80}, the
{CRAY-2}, and the {IBM 3090 VF}",
institution = "Rutherford Appleton Laboratory",
type = "",
number = "RAL-90-083",
kwds = "nla, lud, prll, vect"
}
-db- -dc- -dd- -de-
@article{dbpi:77,
author = "de Boor, C. and A. Pinkus",
year = "1977",
title = "A Backward Error Analysis for Totally Positive Linear Systems",
journal = "Numerische Mathematik",
volume = "27",
pages = "485--490",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, rounding error, totally positive matrix"
}
@article{dece:72,
author = "H. P. Decell",
year = "1972",
title = "On the Derivative of the Generalized Inverse of
a Matrix",
journal = "Linear and Multilinear Algebra",
volume = "1",
pages = "357--359",
kwds = "la, ginv, pert, matrix derivative"
}
@article{dgro:90,
author = "R. D. DeGroat and R. A. Roberts",
year = "1990",
title = "Efficient Numerically Stabilized Rank-One
Eigenstructure Updating",
journal = "IEEE Transactions on Acoustics, Speech, and
Signal Processing",
volume = "38",
pages = "301--316",
kwds = "nla, eig, orthogonalization, update"
}
@article{dent:83,
author = "P. Deift and T. Nande and C. Tome",
year = "1983",
title = "Ordinary Differential Equations and the Symmetric Eigenvalue
Problem",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "1--22",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, symmetric matrix, ode"
}
@article{ddlt:91,
author = "P. Deift and J. Demmel and L.-C. Li and C. Tomei",
year = "1991",
title = "The Bidiagonal Singular Value Decomposition and
{Hamiltonian} Mechanics",
journal = "SIAM Journal on Numerical Analysis",
volume = "28",
pages = "1463--1516",
kwds = "nla, flow algorithm, svd, bidiagonal matrix"
}
@article{detr:71,
author = "T. J. Dekker and J. F. Traub",
year = "1971",
title = "The Shifted {QR}~Algorithm for {Hermitian} Matrices",
journal = "Linear Algebra and Its Applications",
volume = "4",
pages = "137--154",
kwds = "nla, eig, QR algorithm, symmetric matrix"
}
@article{deip:86,
author = "J.-M. Delosme and I. C. F. Ipsen",
year = "1986",
title = "Parallel Solution of Symmetric Positive Definite
Systems with Hyperbolic Rotations",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "75--111",
kwds = "nla, lud, hyperbolic transformation, updating"
}
@article{deba:79,
author = "L.M. Delves and I. Barrodale",
year = "1979",
title = "A Fast Direct Method for the Least Squares Solution of Slightly
Overdetermined Sets of Linear Equations",
journal = "J. of the Inst. Maths. Applics.",
volume = "24",
pages = "149--156",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lud, lsq"
}
@article{dees:82,
author = "R. S. Dembo and S. C. Eisenstat and T. Steihaug",
year = "1982",
title = "Inexact {Newton} Methods",
journal = "SIAM Journal on Numerical Analysis",
volume = "19",
pages = "400--408",
kwds = "nlop, Newton's method"
}
@phdthesis{demm:83,
author = "J. Demmel",
year = "1983",
title = "A Numerical Analyst's {Jordan} Canonical Form",
school = "Department of Computer Science, University of
California at Berleley",
note = "Center for Pure and Applied Mathematics Technical
Report PAM-156",
kwds = "nla, eig, Jordan form, stochastic analysis"
}
@article{demm:83a,
author = "J. W. Demmel",
year = "1983",
title = "The Condition Number of Equivalence Transformations that Block
Diagonalize Matrix Pencils",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "599--610",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, block diagonal matrix, condition"
}
@techreport{deka:84,
Author = "J. Demmel and B. K{\aa}gstr{\"o}m",
year = "1984",
title = "Stable Eigendecompositions of Matrix Pencils",
institution = "Institute of Information Processing, University
of Ume{\aa}",
type = "Report",
number = "UMINF-118.84",
kwds = "nla, geig, matrix pencil"
}
@article{demm:84,
author = "J. W. Demmel",
year = "1984",
title = "Underflow and the Reliability of Numerical Software",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "5",
pages = "887--919",
note = "Cited in \cite{govl:89}.",
kwds = "nla, computer arithmetic"
}
@inproceedings{deka:86,
author = "J. Demmel and B. K{\aa}gstr{\"o}m",
year = "1986",
title = "Stably Computing the {Kronecker} Structure and Reducing
Subspaces of Singular Pencils {$A-\lambda B$} for Uncertain
Data",
booktitle = "Large Scale Eigenvalue Problems",
editor = "J. Cullum and R. A. Willoughby",
pages = "283--323",
publisher = "Elsevier",
address = "",
kwds = "nla, geig, Kronecker form, reducing subspace, matrix pencil"
}
@inproceedings{deka:86a,
author = "J. Demmel and B. K{\aa}gstr{\"o}m",
year = "1986",
title = "Accurage Solutions of Ill-Posed Problems in Control Theory",
booktitle = "Proceedings of the 25th IEEE Conference on Decision and
Control",
pages = "558--563",
publisher = "IEEE",
kwds = "nla, control, ill-posed problem"
}
@article{demm:87,
author = "J. Demmel",
year = "1987",
title = "On Condition Numbers and the Distance to the
Nearest Ill-Posed Problem",
journal = "Numerische Mathematik",
volume = "51",
pages = "251-290",
kwds = "math, la, nla, condition, pert, ill-posed problem"
}
@article{demm:87a,
author = "J. Demmel",
year = "1987",
title = "The Smallest Perturbation of a Submatrix which Lowers the Rank and
Constrained Total Least Squares Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "24",
pages = "199-206",
kwds = "la, matrix approximation, Schmidt-Mirsky theorem,
total least squares, constraints"
}
@inproceedings{demm:87b,
author = "J. Demmel",
year = "1987",
title = "On Error Analysis in Arithmetic with Varying Relative
Precision",
booktitle = "Proceeding of the Eighth Symposium on Computer
Arithmetic",
pages = "148--152",
publisher = "IEEE Computer Society",
address = "Washington, DC",
kwds = "na, rounding error, computer arithmetic"
}
@article{demm:87c,
author = "J. W. Demmel",
year = "1987",
title = "A Counterexample for two Conjectures About Stability",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-32",
pages = "340--342",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, control"
}
@article{demm:87d,
author = "J. W. Demmel",
year = "1987",
title = "Three Methods for Refining Estimates of Invariant Subspaces",
journal = "Computing",
volume = "38",
pages = "43--57",
note = "Cited in \cite{govl:89}.",
kwds = "nla, invariant subspace, iterative refinement, eig"
}
@article{deka:87,
author = "J. Demmel and B. K{\aa}gstr{\"o}m",
year = "1987",
title = "Computing Stable Eigendecompositions of Matrix Pencils",
journal = "Linear Algebra and Its Applications",
volume = "88/89",
pages = "139--186",
kwds = "nla, geig, matrix pencil"
}
@article{demm:88,
author = "J. Demmel",
year = "1988",
title = "The Probability That A Numerical Analysis Problem
Is Difficult",
journal = "Mathematics of Computation",
volume = "50",
pages = "449-480",
kwds = "na, pert, eig, lsq"
}
@article{deka:88,
author = "J. Demmel and B. K{\aa}gstr{\"o}m",
year = "1988",
title = "Accurate Solutions of Ill-Posed Problems in Control Theory",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "9",
pages = "126--145",
kwds = "nla, control, ill-posed problem"
}
@techreport{deve:89,
author = "J. Demmel and K. Veseli{\'c}",
year = "1989",
title = "{Jacobi}'s Method is More Accurate Than {QR}",
institution = "Computer Science Department, New York University",
type = "Technical Report",
number = "468",
kwds = "nla, eig, Jacobi's method, QR algorithm, rounding error,
symmetric matrix"
}
@article{deka:90,
author = "J. Demmel and W. Kahan",
year = "1989",
title = "Accurate Singular Values of Bidiagonal Matrices",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "11",
pages = "873--912",
kwds = "nla, svd, bidiagonal matrix, rounding error"
}
@article{dehi:92,
author = "J. Demmel and N. J. Higham",
year = "1992",
title = "Improved Error Bounds for Underdetermined System Solvers",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "13",
pages = "??--??",
kwds ="uds, rounding error"
}
@article{dehi:92,
author = "J. Demmel and N. J. Higham",
year = "1992",
title = "Improved Error Bounds for Underdetermined System Solvers",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "??--??",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds ="uds, err"
}
@techreport{dehs:92,
author = "J. Demmel and N. J. Higham and R. S. Schreiber",
year = "1992",
title = "Block {LU}~Factorization",
institution = "Department of Mathematics, University of Manchester",
type = "Numerical Analysis Report",
number = "207",
kwds = "nla, lud, block algorithm"
}
@techreport{dmoo:90,
author = "De Moor, Bart",
year = "1990",
title = "The Singular Value Decomposition of Long and Short
Spaces of Noisy Matrices",
institution = "ESAT, Department of Electrical Engineering,
Katholieke Universiteit Leuven",
type = "ESTAT-SISTA Report",
number = "1990-38",
kwds = "la, rank determination, random matrix, la"
}
@article{dmoo:91,
author = "De Moor, Bart",
year = "1991",
title = "A Tree of Generalizations of the Ordinary Singular
Value Decomposition",
journal = "Linear Algebra and Its Applications",
volume = "147",
pages = "469--500",
kwds = "nla, gsvd"
}
@book{demp:69,
author = "A. P. Dempster",
year = "1969",
title = "Elements of Continuous Multivariate Analysis",
publisher = "Addison-Wesley",
address = "Reading, Massachusetts",
kwds = "book, stat, regr, multivariate analysis"
}
@inproceedings{denn:79,
author = "J. B. Dennis",
year = "1979",
title = "The Varieties of Data Flow Computers",
booktitle = "Proceedings of the First Conference on Distributed
Computing Systems",
editor = "",
pages = "",
publisher = "IEEE Computer Society",
address = "",
kwds = "prll, data flow"
}
@article{denn:80,
author = "J. B. Dennis",
year = "1980",
title = "Data Flow Supercomputers",
journal = "Computer",
volume = "",
pages = "48--56",
kwds = "prll, data flow"
}
@techreport{detw:71,
author = "J. E. Dennis and J. F. Traub and R. P. Weber",
year = "1971",
title = "On the Matrix Polynomial, Lambda-Matrix and
Block Eigenvalue Problems",
institution = "Department of Computer Science, Cornell University",
type = "Technical Report",
number = "71-109",
kwds = "la, eig, geig, lambda matrix, matrix polynomial"
}
@unpublished{detw:73,
author = "J. E. Dennis and J. F. Traub and R. P. Weber",
year = "1973",
title = "The Algebraic Theorey of Matrix Polynomials",
note = "Manuscript",
kwds = "la, eig, geig, lambda matrix, matrix polynomial"
}
@article{demo:77,
author = "J. E. Dennis and J. J. Mor{\'e}",
year = "1977",
title = "Quasi-{Newton} Methods, Motivations and Theory",
journal = "SIAM Review",
volume = "19",
pages = "46--89",
kwds = "math, nlop, quasi-Newton, updating, projection"
}
@inproceedings{denn:77,
author = "J. E. Dennis",
year = "1977",
title = "Nonlinear Least Squares and Equations",
pages = "269--312",
booktitle = "The State of the Art in Numerical Analysis",
editor = " D. A. H. Jacobs",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{detw:78,
author = "J. E. Dennis and J. F. Traub and R. P. Weber",
year = "1978",
title = "Algorithms for Solvents of Matrix Polynomials",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "523--533",
kwds = "nla, lambda matrix, matrix polynomial"
}
@article{desc:79,
author = "J. E. Dennis and R. B. Schnabel",
year = "1979",
title = "Least Change Secant Updates for Quasi-{Newton} Methods",
journal = "SIAM Review",
volume = "21",
pages = "443-459",
kwds = "math, nlop, quasi-Newton, updating, projection"
}
@article{degw:81,
author = "J.E. Dennis and D.M. Gay and R.E. Welsh",
year = "1981",
title = "An Adaptive Nonlinear Least-squares Algorithm",
journal = "ACM Transactions on Mathematical Software",
volume = "7",
pages = "348--368",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{degw:81a,
author = "J. E. Dennis and D. M. Gay and R. E. Welsh",
year = "1981",
title = "Algorithm 573 {NL2SOL}: An Adaptive Nonlinear Least-squares
Algorithm",
journal = "ACM Transactions on Mathematical Software",
volume = "7",
pages = "369--383",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, software"
}
@article{degw:83,
author = "J. E. Dennis and D. M. Gay and R. E. Welsh",
year = "1983",
title = "Remark on Algorithm 573",
journal = "ACM Transactions on Mathematical Software",
volume = "9",
pages = "139",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, software"
}
@book{desc:83,
author = "J. E. Dennis and R. B. Schnabel",
year = "1983",
title = "Numerical Methods for Unconstrained Optimization
and Nonlinear Equations",
publisher = "Prentice-Hall",
address = "Englewook Cliffs, New Jersey",
kwds = "book, nlop, quasi-Newton"
}
@article{dest:86,
author = "J.E. Dennis and T. Steihaug",
year = "1986",
title = "On the Successive Projection Approach to Least Squares Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "23",
pages = "717--733",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, projection method, sparse, prll"
}
@article{detu:87,
author = "J. E. Dennis Jr and K. Turner",
year = "1987",
title = "Generalized Conjugate Directions",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "187--209",
note = "Cited in \cite{govl:89}.",
kwds = "nlop, conjugate direction"
}
@article{desc:63,
author = "J. Descloux",
year = "1963",
title = "Bounds for the Spectral Norm of Functions of Matrices",
journal = "Numerische Mathematik",
volume = "5",
pages = "185--190",
note = "Cited in \cite{govl:89}.",
kwds = "nla, norm, matrix function, pert"
}
@article{desp:1887,
author = "J. Desplanques",
year = "1887",
title = "Th\'eor\`eme d'alg\`ebra",
journal = "J. de Math. Spec.",
volume = "9",
pages = "12--13",
note = "Cited in \cite{mami:64}.",
kwds = "la, pert, diagonal dominance"
}
@inproceedings{deap:78,
author = "P. Deuflhard and V. Apostolescu",
year = "1978",
title = "An Underrelaxed {Gauss-Newton} Method for Equality Constrained
Nonlinear Least Squares",
booktitle = "In Proceedings 8th IFIP Conference on Optimization Techniques",
editor = "J. Stoer",
publisher = "Springer Verlag",
volume = "7",
pages = "22--32",
address = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, constraints"
}
@article{defk:87,
author = "P. Deuflhard and B. Fiedler and P. Kunkel",
year = "1987",
title = "Efficient Numerical Pathfollowing Beyond
Critical Points",
journal = "SIAM Journal on Numerical Analysis",
volume = "24",
pages = "912-927",
kwds = "math, nlop, continuation"
}
@article{dvwi:74,
author = "de Villers, E. v. d. S. and L. B. Wilson",
year = "1974",
title = "Hashing the Subscripts of a Sparse Matrix",
journal = "BIT",
volume = "14",
pages = "347--358",
kwds = "nla, sparse, hashing"
}
-df- -dg-
@inproceedings{dgdo:91,
author = "R. D. DeGroad and E. M. Dowling",
year = "1991",
title = "Non-Iterative Subspace Updating",
booktitle = "SPIE Advanced Signal Processing Algorithms,
Architectures, and Implementations II",
editor = "",
pages = "376--387",
publisher = "",
address = "",
note = "Cited in \cite{dgdo:92}.",
kwds = "nla, eig, updating"
}
@unpublished{dgdo:92,
author = "R. D. DeGroad and E. M. Dowling",
year = "1992",
title = "Adaptation Dynamics of the Spherical Subspace Tracker",
note = "Manuscript, Erik Johnson School of Engineering and
Computer Science, University of Texas, Dallas. To
Appear in {\it IEEE Transactions on Signal Processing.\/}",
kwds = "nla, eig, updating"
}
-dh- -di-
@article{dife:76,
author = "M. A. Diamond and D. L. V. Ferreira",
year = "1976",
title = "On a Cyclic Reduction Method for the Solution of {P}oisson's
Equation",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "13",
pages = "54--70",
note = "Cited in \cite{govl:89}.",
kwds = "nla, direct Poisson solver, cyclic reduction"
}
@article{dirs:69,
author = "H. Dirschmid",
year = "1969",
title = " {Bemerkungen zu einer Arbeit von G. Polya
zur Bestimmung der Nullstellen ganzer Funktionen}",
journal = "Numerische Mathematik",
volume = "13",
pages = "344--348",
kwds = "nlop"
}
-dj- -dk- -dl- -dm-
@article{dmgo:91,
author = "De Moor, B. L. R. and G. H. Golub",
year = "1991",
title = "The Restricted Singular Value Decomposition:
Properties and Applications",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "401--425",
kwds = "nla, gsvd"
}
-dn- -do-
@techreport{doms:81,
author = "S. L. Dodd and D. F. McAllister and W. J. Stewart",
year = "1981",
title = "An Iterative Method for the Exact Solution of General
Queueing Networks",
institution = "Computer Studies, North Carolina State University",
type = "Technical Report",
number = "TR 81-04",
kwds = "nla, Markov chain, eig, iter"
}
@article{dosc:87,
author = "J. R. Donaldson and R. B. Schnabel",
year = "1987",
title = "Computational Experience with Confidence Regions and
Confidence Intervals for Nonlinear Least Squares",
journal = "Technometrics",
volume = "29",
pages = "67--82",
kwds = "stat, nlop, regr, hypothesis testing, nllsq"
}
@book{dbms:79,
author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart",
year = "1979",
title = "LINPACK User's Guide",
publisher = "SIAM",
address = "Philadelphia",
kwds = "book, math, nla, linpack, software, lud, qrd, svd,
Cholesky decomposition, updating"
}
@article{dong:83,
author = "J. J. Dongarra",
year = "1983",
title = "Improving the Accuracy of Computed Singular Values",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "4",
pages = "712--719",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, iterative refinement"
}
@article{domw:83,
author = "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
year = "1983",
title = "Improving the Accuracy of Computed Eigenvalues and Eigenvectors",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "23--46",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, iterative refinement"
}
@article{doei:84,
author = "J. J. Dongarra and S. C. Eisenstat",
year = "1984",
title = "Squeezing the Most out of an Algorithm in {CRAY FORTRAN}",
journal = "ACM Transactions on
Mathematical Software",
volume = "10",
pages = "219--230",
kwds = "nla, cray, vect, fortran"
}
@article{dong:84,
author = "J. J. Dongarra",
year = "1984",
title = "Performance of Various Computers Using Standard Linear
Equations Software in a Fortran Environment",
journal = "SIGNUM Newsletter",
volume = "19",
pages = "23--26",
kwds = "nla, lud, performance, fortran"
}
@techreport{dong:84a,
author = "J. J. Dongarra",
year = "1984",
title = "Performance of Various Computers Using Standard Linear
Equations Software in a {FORTRAN} Environment",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Technical Memorandum",
number = "23",
kwds = "nla, lud, performance, fortran"
}
@article{dosa:84,
author = "J. J. Dongarra and A. H. Sameh",
year = "1984",
title = "On Some Parallel Banded System Solvers",
journal = "Parallel ",
volume = "1",
pages = "223--235",
note = "Cited in \cite{govl:89}.",
kwds = "nla, band matrix, prll"
}
@article{dogk:84,
author = "J. J. Dongarra and F. G. Gustavson and A. Karp",
year = "1984",
title = "Implementing Linear Algebra Algorithms for Dense Matrices on a
Vector Pipeline Machine",
journal = "{SIAM} Review",
volume = "26",
pages = "91--112",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vect"
}
@article{dohi:84,
author = "J. J. Dongarra and R. E. Hiromoto",
year = "1984",
title = "A Collection of Parallel Linear Equation Routines for the
{D}enelcor {HEP}",
journal = "Parallel ",
volume = "1",
pages = "133--142",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, lud"
}
@article{doso:86,
author = "J. J. Dongarra and D. C. Sorensen",
year = "1986",
title = "Linear Algebra on High Performance Computers",
journal = "Appl. Math. and Comp.",
volume = "20",
pages = "57--88",
note = "Cited in \cite{govl:89}",
kwds = "nla, performance, vect"
}
@article{dohe:86,
author = "J. Dongarra and T. Hewitt",
year = "1986",
title = "Implementing Dense Linear Algebra Algorithms Using Multitasking on
the {Cray X-MP-4} (or Approaching the Gigaflop)",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "7",
pages = "347--350",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, vect"
}
@article{dokh:86,
author = "J. J. Dongarra and L. Kaufman and S. Hammarling",
year = "1986",
title = "Squeezing the Most Out of Eigenvalue Solvers on High Performance
Computers",
journal = "Linear Algebra and its Applications",
volume = "77",
pages = "113--136",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, vect"
}
@article{doss:86,
author = "J. J. Dongarra and A. Sameh and D. Sorensen",
year = "1986",
title = "Implementation of Some Concurrent Algorithms for Matrix
Factorization",
journal = "Parallel Computing",
volume = "3",
pages = "25--34",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, lud, qrd"
}
@article{dddh:87,
author = "J. J. Dongarra and Du Croz, J.
and I. Duff and S. Hammarling",
year = "1987",
title = "A Proposal for a Set of Level 3 Basic Linear
Algebra Subprograms",
journal = "SIGNUM Newsletter",
volume = "22",
pages = "2-14",
kwds = "nla, prll, blas, memory hierarchy, software"
}
@article{doso:87,
author = "J. J. Dongarra and D. C. Sorensen",
year = "1987",
title = "A Fully Parallel Algorithm for the Symmetric
Eigenvalue Problem",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "s139--s154",
kwds = "nla, eig, symmetric matrix, prll"
}
@article{doso:87a,
author = "J. J. Dongarra and D. C. Sorensen",
year = "1987",
title = "A Portable Environment for Developing Parallel Programs",
journal = "Parallel ",
volume = "5",
pages = "175--186",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll"
}
@techreport{dohs:87,
author = "J. J. Dongarra and S. Hammarling and D. C. Sorensen",
year = "1987",
title = "Block Reduction of Matrices to Condensed form for Eigenvalue
Computations",
number = "ANL-MCS-TM 99",
institution = "Argonne National Laboratory",
address = "Argonne, Illinois",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, eig"
}
@article{ddhh:88,
author = "J. J. Dongarra and Du Croz, J. and
S. Hammarling and R. J. Hanson",
year = "1988",
title = "An Extended Set of Fortran Basic Linear Algebra
Subprograms",
journal = "ACM Transactions on Mathematical Software",
volume = "14",
pages = "1--17",
kwds = "nla, blas, vect, software"
}
@article{ddhh:88a,
author = "J. J. Dongarra and Du Croz, J. and
S. Hammarling and R. J. Hanson",
year = "1988",
title = "An Extended Set of Fortran Basic Linear Algebra
Subprograms: Model Implementation and Test Programs",
journal = "ACM Transactions on Mathematical Software",
volume = "14",
pages = "18--32",
kwds = "nla, blas, vect, software"
}
@techreport{dosi:91,
author = "J. J. Dongarra and M. Sidani",
year = "1991",
title = "A Parallel Algorithm for the Non-Symmetric Eigenvalue
Problem",
institution = "Mathematical Sciences Section, Oak Ridge National
Laboratory",
type = "Report",
number = "ORNL/TM-12003",
kwds = "nla, prll, eig, nonsymmetric matrix"
}
@techreport{dovg:92,
author = "J. J. Dongarra and M. Sidani",
year = "1992",
title = "Reduction to Condensed Form for the Eigenvalue Problem
on Distributed Memory Architectures",
institution = "Mathematical Sciences Section, Oak Ridge National
Laboratory",
type = "Report",
number = "ORNL/TM-12006",
kwds = "nla, prll, eig, nonsymmetric matrix"
}
@incollection{dool:1878,
author = "M. H. Doolittle",
year = "1878",
title = "Method Employed in the Solution of Normal Equations and
the Adjustment of a Triangulation",
booktitle = "U. S. Coast and Geodetic Survey Report",
pages = "115--120",
note = "Cited in \cite{dwye:51}.",
publisher = "",
kwds = "nla, Doolittle's method, lud, normal equations"
}
@article{dorr:70,
author = "F. W. Dorr",
year = "1970",
title = "The Direct Solution of the Discrete {Poisson} Equation
on a Rectangle",
journal = "SIAM Review",
volume = "12",
pages = "248--263",
kwds = "na, pde, direct Poisson solver"
}
@article{dorr:73,
author = "F. W. Dorr",
year = "1973",
title = "The Direct Solution of the Discrete {P}oisson Equation in
{$O(n^{2})$} Operations",
journal = "{SIAM} Review",
volume = "15",
pages = "412--415",
note = "Cited in \cite{govl:89}.",
kwds = "nla, direct Poisson solver"
}
@article{doug:71,
author = "A. Douglas",
year = "1971",
title = "Examples Concerning Efficient Strategies for {Gaussian}
Elimination",
journal = "Computing",
volume = "8",
pages = "382--394",
kwds = "nla, lud, pivoting"
}
@article{doyl:82,
author = "J. Doyle",
year = "1982",
title = "Analysis of Feedback Systems with Structured Uncertainties",
journal = "IEE Proceedings",
volume = "129",
pages = "242--250",
kwds = "control"
}
-dp- -dq- -dr-
@book{drsm:68,
author = "N. R. Draper and H. Smith",
year = "1968",
title = "Applied Regression Analysis",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr"
}
@book{drsm:81,
author = "N. R. Draper and H. Smith",
year = "1981",
title = "Applied Regression Analysis",
edition = "second",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr"
}
@article{draz:58,
author = "M. P. Drazin",
year = "1958",
title = "Pseudo-Inverses in Associative Rings and Semigroups",
journal = "American Mathematical Monthly",
volume = "65",
pages = "506--514",
kwds = "la, ginv, Drazin generalized inverse"
}
-ds- -dt- -du-
@article{dugr:79,
author = "P. F. Dubois and A. Greenbaum and G. H. Rodrigue",
year = "1979",
title = "Approximating the Inverse of a Matrix for Use on Iterative
Algorithms on Vector Processors",
journal = "Computing",
volume = "22",
pages = "257--268",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, iter, vect"
}
@article{dumw:68,
author = "A. A. Dubrulle and R. S. Martin and J. H. Wilkinson",
year = "1968",
title = "The Implicit {QL}~Algorithm",
journal = "Numerische Mathematik",
volume = "12",
pages = "377--383",
note = "Also in \cite[pp.241--248]{wire:71}.",
kwds = "nla, eig, QR algorithm, QL algorithm, tridiagonal matrix,
software"
}
@article{dubr:72,
author = "A. A. Dubrulle",
year = "1972",
title = "Solution of the Complete Symmetric Eigenproblem in a
Virtual Memory Environment",
journal = "IBM Journal of Research and Development",
volume = "6",
pages = "612--616",
kwds = "nla, eig, performance, symmetric matrix"
}
@article{dubr:91,
author = "A. A. Dubrulle",
year = "1991",
title = "Block Gauss Reduction to Hessenberg Form",
journal = "SIAM Journal on Scientific and Statistical Computation",
volume = "12",
pages = "1245--1252",
kwds = "nla, eig, Hessenberg matrix, block algorithm"
}
@techreport{dnrt:78,
author = "Du Croz, J. J. and S. M. Nugent and J. K. Reid and
D. B. Taylor",
year = "1978",
title = "Solving Large Full Sets of Linear Equations in a
Paged Virtual Store",
institution = "Computer Science and Systems Division, AERE Harwell",
type = "Technical Report",
number = "CSS 68",
kwds = "nla, lud, memory hierarchy"
}
@article{dure:74,
author = "I. S. Duff and J. K Reid",
year = "1974",
title = "A Comparison of Sparsity Orderings for Obtaining a
Pivotal Sequence in {Gaussian} Elimination",
journal = "J. Inst. Maths. Applics.",
volume = "14",
pages = "281--291",
kwds = "nla, lud, sparse, pivoting"
}
@article{duff:74,
author = "I. S. Duff",
year = "1974",
title = "Pivot Selection and Row Orderings in {Givens} Reduction on Sparse
Matrices",
journal = "Computing",
volume = "13",
pages = "239--248",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, sparse"
}
@article{dure:75,
author = "I. S. Duff and J. K. Reid",
year = "1975",
title = "On the Reduction of Sparse Matrices to Condensed Forms by
Similarity Transformations",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "15",
pages = "217--224",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, sparse"
}
@article{dure:76,
author = "I. S. Duff and J. K. Reid",
year = "1976",
title = "A Comparison of Some Methods for the Solution of Sparse
Overdetermined Systems of Linear Equations",
journal = "J. Inst. Maths. Applics.",
volume = "17",
pages = "267--280",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{duff:77,
author = "I. S. Duff",
year = "1977",
title = "A Survey of Sparse Matrix Research",
journal = "Proceedings of the {IEEE}",
volume = "65",
pages = "500--535",
note = "Cited in \cite{govl:89}.",
kwds = "nla, sparse"
}
@proceedings{dust:79,
editor = "I. S. Duff and G. W. Stewart",
year = "1979",
title = "Sparse Matrix Proceedings 1978",
publisher = "SIAM",
address = "Philadelphia",
kwds = "nla, sparse"
}
@article{dumn:79,
author = "I. S. Duff and N. Munksgaard and H. B. Nielsen and J. K. Reid",
year = "1979",
title = "Direct Solution of Sets of Linear Equations whose Matrix is
Sparse Symmetric and Indefinite",
journal = "J. Inst. Maths. Applics.",
volume = "23",
pages = "235--250",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, indefinite system, symmetric matrix, sparse"
}
@techreport{dure:82,
author = "I. S. Duff and J. K. Reid",
year = "1982",
title = "{MA27}---A Set of {Fortran} Subroutines for Solving Sparse
Symmetric Sets of Linear Equations",
institution = "AERE, Harwell, England",
type = "Technical Report",
number = "R.10533",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, symmetric matrix"
}
@article{dure:83,
author = "I. S. Duff and J. K. Reid",
year = "1983",
title = "The Multifrontal Solution of Indefinite Sparse Symmetric
Linear Systems",
journal = "ACM Transactions on Mathematical Software",
volume = "9",
pages = "302--325",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, indefinite system, sparse, symmetric matrix"
}
@book{duer:86,
author = "I. S. Duff and A. M. Erisman and J. K. Reid",
year = "1986",
title = "Direct Methods for Sparse Matrices",
publisher = "Clarendon Press",
address = "Oxford",
kwds = "book, math, nla, sparse"
}
@article{dugl:89,
author = "I. S. Duff and R. G. Grimes and J. G. Lewis",
year = "1989",
title = "Sparse Matrix Test Problems",
journal = "ACM Transactions on Mathematical Software",
volume = "15",
pages = "1--14",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, software"
}
@article{duha:55,
author = "L. Dulmage and I. Halperin",
year = "1955",
title = "On a Theorem of {Frobenius--K\"onig} and {J.~von~Neuman's}
Game of Hide and Seek",
journal = "Transactions of the Royal Society of Canada, Section~3,
Third Series",
volume = "49",
pages = "23--25",
kwds = "la, nla, Frobenius-Koenig theorem"
}
@book{dusc:58,
author = "N. Dunford and J. Schwartz",
year = "1958",
title = "Linear Operators, Part {I}",
publisher = "Interscience",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "book, math"
}
@article{durb:60,
author = "J. Durbin",
year = "1960",
title = "The Fitting of Time Series Models",
journal = "Review of the International Statisical Institute",
volume = "28",
pages = "233--243",
note = "Cited in \cite{govl:89}.",
kwds = "stat, time series"
}
-dv- -dw-
@article{dwye:44,
author = "P. S. Dwyer",
year = "1944",
title = "A Matrix Presentation of Least Squares and Correllation Theory
with Matrix Justification of Improved Methods of Solution",
journal = "Annals of Mathematical Statistics",
volume = "15",
pages = "82-89",
kwds = "stat, la, lsq, regr"
}
@article{dwye:45,
author = "P. Dwyer",
year = "1945",
title = "The Square Root Method and its Use in Correlation and Regression",
journal = " Journal of the American Statistical Association",
volume = "40",
pages = "493--503",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, regr, lsq, Cholesky decomposition"
}
@article{dwma:48,
author = "P. S. Dwyer and M. S. Macphail",
year = "1948",
title = "Symbolic Matrix Derivatives",
journal = "Annals of Mathematical Statistics",
volume = "19",
pages = "517-534",
kwds = "stat, la, matrix derivative"
}
@book{dwye:51,
author = "P. S. Dwyer",
year = "1951",
title = "Linear Computations",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, nla, lsq, regr, linear system"
}
-dx- -dy- -dz-
-ea-
@book{eato:83,
author = "M. L. Eaton",
year = "1983",
title = "Multivariate Statistics",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, multivariate analysis"
}
-eb-
@article{eber:62,
author = "P. J. Eberlein",
year = "1962",
title = "A {Jacobi}-Like Method for the Automatic Computation
of Eigenvalues and Eigenvectors of an Arbitrary Matrix",
journal = "Journal of the Society of Industrial and Applied Mathematics",
volume = "10",
pages = "74--88",
kwds = "nla, Jacobi-like, eig, nonsymmetric matrix"
}
@article{eber:65,
author = "P. J. Eberlein",
year = "1965",
title = "On Measures of Non-normality for Matrices",
journal = "American Mathematical Monthly",
volume = "72",
pages = "995--996",
note = "Cited in \cite{govl:89}.",
kwds = "la, normal matrix, pert"
}
@article{ebbo:68,
author = "P. J. Eberlein and J. Boothroyd",
year = "1968",
title = "Solution to the Eigenproblem by a Norm Reducing
{Jacobi} Type Method",
journal = "Numerische Mathematik",
volume = "11",
pages = "1--12",
note = "Also in \cite[pp.327--338]{wire:71}.",
kwds = "nla, eig, Jacobi-like, nonsymmetric matrix, software"
}
@article{eber:70,
author = "P. J. Eberlein",
year = "1970",
title = "Solution to the Complex Eigenproblem by a Norm
Reducing {Jacobi} Type Method",
journal = "Numericshe Mathematik",
volume = "14",
pages = "232--245",
note = "Also in \cite[pp.404--417]{wire:71}.",
kwds = "nla, eig, Jacobi-like, nonsymmetric matrix, software"
}
@article{eber:71,
author = "P. J. Eberlein",
year = "1971",
title = "On the Diagonalization of Complex Symmetric Matrices",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "7",
pages = "377--383",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, symmetric matrix, complex matrix"
}
@article{ebhu:75,
author = "P. J. Eberlein and C. P. Huang",
year = "1975",
title = "Global Convergence of the {$QR$}~Algorithm
for Unitary Matrices with Some Results for
Normal Matrices",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "97--104",
kwds = "nla, eig, QR algorithm, normal matrix, orthogonal matrix"
}
@incollection{eber:87,
author = "P. J. Eberlein",
year = "1987",
title = "On Using the {J}acobi Method on a Hypercube",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = "{SIAM} Publications",
address = "Philadelphia",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, prll, hypercube"
}
-ec-
@article{ecyo:36,
author = "C. Eckart and G. Young",
year = "1936",
title = "The Approximation of One Matrix by Another of Lower Rank",
journal = "Psychometrika",
volume = "1",
pages = "211-218",
kwds = "stat, la, svd, matrix approximation, Schmidt-Mirsky theorem"
}
@article{ecyo:39,
author = "C. Eckart and G. Young",
year = "1939",
title = "A Principal Axis Transformation for Non-{Hermitian} Matrices",
journal = "Bulletin of the American Mathematical Society",
volume = "45",
pages = "118-121",
kwds = "math, la, svd"
}
-ed-
@techreport{edel:89,
author = "A. Edelman",
year = "1989",
title = "Eigenvalues and Condition Numbers of Random Matrices",
institution = "Department of Mathematics, Massachusetts Institute
of Technology",
type = "Numerical Analysis Report",
number = "89--7",
kwds = "la, random matrix, condition, eig"
}
@proceedings{eddy:81,
editor = "W. F. Eddy",
year = "1981",
title = "Computer Science and Statistics: Proceedings of the Eighteenth
Symposium on the Interface",
publisher = "Springer",
address = "New York",
kwds = "stat, cs"
}
-ef-
@incollection{efro:60,
author = "M. A. Efroymsen",
year = "1960",
title = "Multiple Regression Analysis",
booktitle = "Mathematical Methods for Digital Computers",
publisher = "",
kwds = "math, nla, regr, lsq, sweep operator, software"
}
-eg-
@techreport{eghl:80,
author = "P. P. B. Eggermont and G. T. Herman and A. Lent",
year = "1980",
title = "Iterative Algorithms for Large Partitioned Linear
Systems, with Applications to Image Reconstruction",
institution = "Medical Image Processing Group,
Department of Computer Science, State University of
New York at Buffalo",
type = "Technical Report",
number = "MIPG40",
kwds = "nla, linear system, iter, sparse"
}
@article{egge:1876,
author = "H. Eggers",
year = "1876",
title = "Calculation of Radicals",
journal = "The Analyst",
volume = "3",
pages = "100--102",
kwds = "nlop, polynomial"
}
@article{egge:1876a,
author = "H. Eggers",
year = "1876",
title = "A New Method of Solving Numerical Equations",
journal = "The Analyst",
volume = "3",
pages = "100--102",
kwds = "nlop, polynomial"
}
-eh-
@article{ehrm:60,
author = "H. Ehrmann",
year = "1960?",
title = " {Konstruktion und Durchf\"uhrung von Iterationsverfahren
h\"oherer Ordnung}",
journal = "Arch. Rational Mech. Anal.",
volume = "4",
pages = "65--88",
kwds = "nlop"
}
-ei-
@techreport{eila:75,
author = "E. L. Eichhorn and C. L. Lawson",
year = "1975",
title = "An {ALGOL} Procedure for Solution of Constrained Least
Squares Problems",
institution = "JPL, Pasadena, California",
type = "Computing Memorandum",
number = "No. 374",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints, software"
}
@article{eini:83,
author = "M. Eiermann and W. Niethammer",
year = "1983",
title = "On the Construction of Semi-iterative Methods",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "1153--1160",
note = "Cited in \cite{govl:89}.",
kwds = "nla, iter, sparse"
}
@article{eina:74,
author = "B. Einarsson",
year = "1974",
title = "Bibliography on the Evaluation of Numerical Software",
journal = "Journal of Computational and Applied Mathematics",
volume = "5",
pages = "145-159",
kwds = "na, software"
}
@inbook{eise:68,
author = "C. Eisenhart",
year = "1968",
title = "{Gauss, Carl Friedrich}",
booktitle = "International Encyclopedia of the Social Sciences",
volume = "6",
pages = "74-81",
kwds = "stat, Gauss, history"
}
@article{eiss:81,
author = "S. C. Eisenstat and M. H. Schultz and A. H. Shcerman",
year = "1981",
title = "Algorithms and Data Structures for Sparse Symmetric
{Gaussian} Elimination",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "225--237",
kwds = "nla, lud, sparse, symmetric matrix"
}
@article{eise:81,
author = "S. Eisenstat",
year = "1981",
title = "Efficient Implementation of a Class of Preconditioned
Conjugate Gradient Methods",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "1--4",
kwds = "nla, conjugate gradients, preconditioning"
}
@article{egss:82,
author = "S. C. Eisenstat and M. C. Gursky and M. H. Schultz
and A. H. Sherman",
year = "1982",
title = "Yale Sparse Matrix Package {I}: The Symmetric Codes",
journal = "International Journal for Numerical Methods in Engineering",
volume = "18",
pages = "1145--1151",
kwds = "nla, lud, sparse, symmetric matrix, software"
}
@article{eise:84,
author = "S. C. Eisenstat",
year = "1984",
title = "Efficient Implementation of a Class of Preconditioned Conjugate
Gradient Methods",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "2",
pages = "1--4",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning"
}
@article{ehhr:88,
author = "S. C. Eisenstat and M. T. Heath and C. S. Henkel and
C. H. Romine",
year = "1988",
title = "Modified Cyclic Algorithms for Solving Triangular
Systems on Distributed-Memory Multiprocessors",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "589--600",
kwds = "nla, prll, triangular matrix"
}
-ej- -ek-
@phdthesis{ekbl:74,
author = "H. Ekblom",
year = "1974",
title = "Lp-Methods for Robust Regression",
school = "Lund University",
kwds = "nlop, stat, regr, robust estimation"
}
@article{ekbl:73,
author = "H. Ekblom",
year = "1973",
title = "Calculation of Linear Best $\ell_p$-Approximations",
journal = "BIT",
volume = "13",
pages = "292--300",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, robust estimation, lsq, regr, Hoelder approximation"
}
-el-
@article{elde:77,
author = "L. Eld\'en",
year = "1983",
title = "Algorithms for the Regularization of Ill-Conditioned Least
Squares Problems",
journal = "BIT",
volume = "17",
pages = "134--145",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, ill-conditioned problem, regularization"
}
@phdthesis{elde:77a,
author = "L. Eld{\`e}n",
year = "1977",
title = "Numerical Analysis of Regularization and Constrained Least Square
Methods",
Number = 20,
school = "Linkoping Studies in Science and Technology",
address = "Linkoping, Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lsq, regularization, constraints"
}
@article{elde:80,
author = "L. Eld\'en",
year = "1980",
title = "Perturbation Theory for the Least Squares Problem with Linear
Equality Constraints",
journal = "SIAM Journal on Numerical Analysis",
volume = "17",
pages = "338-350",
kwds = "la, lsq, pert, constraints"
}
@article{elde:83,
author = "L. Eld\'en",
year = "1983",
title = "A Weighted Pseudoinverse, Generalized Singular Values, and
Constrained Least Squares Problems",
journal = "BIT",
volume = "22",
pages = "487-502",
kwds = "la, nla, lsq, ginv, constraints, weights"
}
@article{elde:84,
author = "L. Eld\'en",
year = "1984",
title = "An Efficient Algorithm for the Regularization of Ill-Conditioned
Least Squares Problems with a Triangular {Toeplitz} Matrix",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "5",
pages = "229--236",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, triangular matrix, Toeplitz matrix, regularization,
ill-conditioned problem"
}
@article{elde:84a,
author = "L. Eld\'en",
year = "1984",
title = "An Algorithm for the Regularization of Ill-Conditioned Banded
Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "5",
pages = "237--254",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, band matrix, regularization, ill-conditioned problem"
}
@article{elde:84b,
author = "L. Eld\'en",
year = "1984",
title = "A Note on the Computation of the Generalized Cross-Validation
Function for Ill-Conditioned Least Squares Problems",
journal = "BIT",
volume = "24",
pages = "467--472",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, ill-conditioned problem, cross validation"
}
@article{elsc:86,
author = "L. Eld\'en and R. Schreiber",
year = "1986",
title = "A Systolic Array for the Regularization of Ill-Conditioned
Least-Squares Problems with Triangular {Toeplitz} Matrix",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "137-147",
kwds = "nla, prll, systolic, Toeplitz matrix, lsq,
triangular matrix, regularization, ill-conditioned problem"
}
@techreport{elde:88,
author = "L. Eld{\`e}n",
year = "1988",
title = "A Parallel {QR} Decomposition Algorithm",
number = "LiTh Mat R 1988-02",
institution = "Mathematics, Linkoping University",
address = "Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, prll"
}
@article{elfv:80,
author = "T. Elfving",
year = "1980",
title = "Block-Iterative Methods for Consistent and Inconsistent
Linear Equations",
journal = "Numerishce Mathematik",
volume = "35",
pages = "1--12",
kwds = "nla, linear system, sparse, iter"
}
@article{elfv:80a,
author = "T. Elfving",
year = "1980",
title = "On Some Methods for Entropy Maximization and Matrix Scaling",
journal = "Linear Algebra and Its Applications",
volume = "34",
pages = "321--339",
kwds = "nla, entropy, scaling"
}
@article{elfv:81,
author = "T. Elfving",
year = "1981",
title = "On the Sensitivity of the Gravity Model",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "2",
pages = "19--24",
kwds = "nlop, gravity model"
}
@article{elma:86,
author = "H. Elman",
year = "1986",
title = "A Stability Analysis of Incomplete {LU} Factorization",
journal = "Mathematics of Computation",
volume = "47",
pages = "191--218",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, rounding error, incomplete factorization,
preconditioning"
}
@article{elsn:82,
author = "L. Elsner",
year = "1982",
title = "On the Variation of the Spectra of Matrices",
journal = "Linear Algebra and Its Applications",
volume = "47",
pages = "127--138",
kwds = "la, pert, eig"
}
@article{elsu:82,
author = "L. Elsner and J.-G. Sun",
year = "1982",
title = "Perturbation Theorems for the Generalized Eigenvalue Problem",
journal = "Linear Algebra and Its Applications",
volume = "48",
pages = "341--357",
kwds = "la, geig, pert"
}
@article{elsn:85,
author = "L. Elsner",
year = "1985",
title = "An Optimal Bound for the Spectral Variation of Two Matrices",
journal = "Linear Algebra and Its Applications",
volume = "71",
pages = "77--80",
kwds = "la, pert, eig"
}
@article{ella:85,
author = "L. Elsner and P. Lancaster",
year = "1985",
title = "The Spectral Variation of Pencils of Matrices",
journal = "Journal of Computational Mathematics",
volume = "3",
pages = "262--274",
kwds = "la, pert, geig, matrix pencil"
}
@article{elhe:91,
author = "L. Elsner and C. He",
year = "1991",
title = "An Algorithm for Computing the Distance to
Uncontroloability",
journal = "Systems and Control Letters",
volume = "17",
pages = "453--464",
kwds = "nla, control, controllability"
}
@inproceedings{elre:88,
author = "A. Elster and A. P. Reeves",
year = "1988",
title = "Block Matrix Operations Using Orthogonal Trees",
booktitle = "The Third Conference on Hypercube Concurrent Computers and
Applications, Vol. {II}, Applications",
editor = "G. Fox",
publisher = "{ACM} Press",
address = "New York",
pages = "1554--1561",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm"
}
-em-
@article{emvd:82,
author = "A. Emami-Naeini and Van Dooren, P.",
year = "1982",
title = "Computation of Zeros of Linear Multivariable Systems",
journal = "Automatica",
volume = "18",
pages = "415--430",
kwds = "nla, geig"
}
@article{empe:70,
author = "P. Empedocles",
year = "1970",
title = "Ground-State Eigenvectors for Many Configuration
Wavefunctions",
journal = "Journal of Computational Physics",
volume = "6",
pages = "113--119",
kwds = "nla, geig, relaxation, symmetric matrix"
}
-en-
@article{enri:79,
author = "W. Enright",
year = "1979",
title = "On the Efficient and Reliable Numerical Solution of Large Linear
Systems of {O. D. E.}'s",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-24",
pages = "905--908",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, sparse"
}
-eo- -ep- -eq- -er-
@article{erru:80,
author = "T. Ericsson and A. Ruhe",
year = "1980",
title = "The Spectral Transformation {Lanczos} Method for the
Numerical Solution of Large Sparse Generalized
Symmetric Eigenvalue Problems",
journal = "Mathematics of Computation",
volume = "35",
pages = "1251--1268",
kwds = "nla, geig, Lanczos algorithm, symmetric matrix"
}
@techreport{eric:82,
author = "Thomas Ericsson",
year = "1982",
title = "Some Properties of the Eigenvectors of a Symmetric
Tridiagonal Matrix",
institution = "Institute of Information Processing, University of
Ume\aa",
type = "Report",
number = "UMINF-99.82",
kwds = "la, eig, tridiagonal matrix, symmetric matrix"
}
@techreport{erik:81,
author = "J. Eriksson",
year = "1981",
title = "Algorithms for Entropy and Mathematical Programming",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Link{\"o}ping Studies in Science and Technology
Dissertations",
number = "63",
kwds = "nlop, entropy"
}
@inproceedings{eris:72,
author = "A. M. Erisman",
year = "1972",
title = "Sparse Matrix Approach to the Frequency Domain Analysis
of Linear Passive Electrical Networks",
booktitle = "Sparse Matrices and Their Applications",
editor = "D. J. Rose and R. A. Willoughby",
pages = "31--40",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, lud, sparse"
}
@article{erre:74,
author = "A. M. Erisman and J. K. Reid",
year = "1974",
title = "Monitoring Stablility of the Triangular Factorization
of a Sparse Matrix",
journal = "Numerische Mathematik",
volume = "22",
pages = "183--186",
kwds = "nla, lud, sparse, pivoting"
}
@article{erti:75,
author = "A. M. Erisman and W. F. Tinney",
year = "1975",
title = "On Computing Certain Elements of the Inverse of a Sparse Matrix",
journal = "Communications of the ACM",
volume = "18",
pages = "177--179",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, inverse matrix"
}
-es- -et- -eu- -ev-
@article{evan:83,
author = "D. J. Evans and R. Dunbar",
year = "1983",
title = "The Parallel Solution of Triangular Systems of Equations",
journal = "{IEEE} Transactions on ",
volume = "C-32",
pages = "201--204",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, triangular matrix, prll"
}
@article{evan:84,
author = "D. J. Evans",
year = "1984",
title = "Parallel {SOR} Iterative Methods",
journal = "Parallel ",
volume = "1",
pages = "3--18",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, relaxation, iter"
}
@techreport{evan:89,
author = "S. P. Evans",
year = "1989",
title = "Transient Analysis of a Virtual Path Shared by
Services with Very Different Characteristics",
institution = "Teletraffic Research Center, University of Adelaide",
type = "TRC Report",
number = "9/89",
kwds = "nla, Markov chain"
}
@article{evli:89,
author = "D. J. Evans and C. Li",
year = "1989",
title = "Numerical Aspects of the Generalized cg-Method Applied to Least
Squares Problems",
journal = "Computing",
volume = "41",
pages = "171--178",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, conjugate gradients"
}
-ew- -ex- -ey- -ez-
-fa-
@article{fama:84,
author = "V. Faber and T. Manteuffel",
year = "1984",
title = "Necessary and Sufficient Conditions for the Existence of a
Conjugate Gradient Method",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "21",
pages = "352--362",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients"
}
@book{fadd:59,
author = "V. N. Faddeeva",
year = "1959",
title = "Computational Methods of Linear Algebra",
publisher = "Dover",
address = "New York",
note = "Translated from the Russian by C. D. Benster.",
kwds = "book, nla"
}
@book{fafa:63,
author = "D. K. Faddeev and V. N. Faddeeva",
year = "1963",
title = "Computational Methods of Linear Alegbra",
publisher = "W. H. Freeman and Co.",
address = "San Francisco",
kwds = "book, nla"
}
@article{fakf:68,
author = "D. K. Faddeev and V. N. Kublanovskaja and V. N. Faddeva",
year = "1968",
title = "Solution of Linear Algebraic Systems with Rectangular
Matrices",
journal = "Trudy Mat. Inst. Steklov",
volume = "96",
pages = "93--111",
kwds = "nla, linear system"
}
@incollection{fakf:68a,
author = "D. K. Faddeev and V. N. Kublanovskaya and V. N. Faddeeva",
year = "1968",
title = "Sur les systemes lineaires algebriques de matrices rectangulaires
et malconditionees",
pages = "161--170",
booktitle = "Programmation en Mathematiques Numeriques",
publisher = "Editions Centre Nat. Recherche Sci.",
address = "Paris VII",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, rank determination"
}
@article{fafa:77,
author = "V. N. Fadeeva and D. K. Fadeev",
year = "1977",
title = "Parallel Calculations in Linear Algebra",
journal = "Kibernetika",
volume = "6",
pages = "28--40",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll"
}
@article{fasc:88,
author = "U. Faigle and R. Schrader",
year = "1988",
title = "On the Convergence of Stationary Distributions in Simulated
Annealing Algorithms",
journal = "Information Processing Letters",
volume = "27",
pages = "189--194",
kwds = "nlop, simulated annealing"
}
@article{falk:64,
author = "S. Falk",
year = "1964",
title = " {Einschliessungss\"atze f\"ur die Eigenwerte
normaler Matrizenpaare}",
journal = " {Zeitschrift f\"ur Angewandte Mathematik und Mechanik}",
volume = "45",
pages = "41--55",
kwds = "la, eig, pert, normal matrix"
}
@article{falk:65,
author = "S. Falk",
year = "1965",
title = " {Einschliessungss\"atze f\"ur die Eigenvektoren
normaler Matrizenpaare}",
journal = " {Zeitschrift f\"ur Angewandte Mathematik und Mechanik}",
volume = "45",
pages = "47--56",
kwds = "la, eig, pert, normal matrix"
}
@article{falk:73,
author = "S. Falk",
year = "1973",
title = " {Berechnung von Eigenwerten und Eigenvektoren normaler
Matrizenpaare durch Ritz-Iteration}",
journal = "{Zeitschrift f\"ur Angewandte Mathematik und Mechanik}",
volume = "53",
pages = "73--91",
kwds = "nla, geig, Rayleigh-Ritz method, symmetric matrix, sparse"
}
@article{fan:51,
author = "K. Fan",
year = "1951",
title = "Maximum Properties and Inequalities for the Eigenvalues of
Completely Continuous Operators.",
journal = "Proceedings of the National Academy of Sciences",
volume = "37",
pages = "760-766",
kwds = "la, eig, norm, pert"
}
@article{faho:55,
author = "K. Fan and A. J. Hoffman",
year = "1955",
title = "Some Metric Inequalities in the Space of Matrices",
journal = "Proceedings of the American Mathematical Society",
volume = "6",
pages = "111-116",
kwds = "la, norm"
}
@inproceedings{fare:85,
author = "R.W. Farebrother",
year = "1985",
title = "The Statistical Estimation of the Standard Linear
Model, 1756--1853",
pages = "77--99",
booktitle = "In Proceedings Proc. First Tampere Sem. Linear Models 1983",
editor = "",
publisher = "",
address = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, regr, history"
}
@book{fare:88,
author = "R.W. Farebrother",
year = "1988",
title = "Linear Least Squares Computations",
publisher = "Marcel Dekker, Inc.",
address = "New York and Basel",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, stat, regr, lsq, history"
}
-fb- -fc- -fd- -fe-
@article{feva:62,
author = "D. B. Feingold and R. S. Varga",
year = "1962",
title = "Block Diagonally Dominant Matrices and Generalizations
of the {Gerschgorin} Circle Theorem",
journal = "Pacific Journal of Mathematics",
volume = "12",
pages = "1241--1250",
kwds = "la, pert, eig, Gerschgorin's theorem"
}
@article{feld:74,
author = "M. Feldstein",
year = "1974",
title = "Errors in Variables: A Consistent Estimator with
Smaller {MSE} in Finite Samples",
journal = "Journal of the American Statistical Association",
volume = "69",
pages = "990--996",
kwds = "stat, regr, eriv"
}
@article{fele:74,
author = "M. G. Feler",
year = "1974",
title = "Calculation of Eigenvectors of Large Matrices",
journal = "Journal of Computational Physics",
volume = "14",
pages = "341--349",
kwds = "nla, eig, sparse"
}
@article{fefo:51,
author = "W. Feller and G. E. Forsythe",
year = "1951",
title = "New Matrix Transformations for Obtaining Characteristic
Vectors",
journal = "Quarterly of Applied Mathematics",
volume = "8",
pages = "325-331",
kwds = "nla, eig, Householder transformation"
}
@book{fell:66,
author = "W. Feller",
year = "1966",
title = "An Introduction to Probability Theory and Its Applications II",
publisher = "John Wiley",
address = "New York",
edition = "second",
kwds = "book, math, stat, probability"
}
@article{fell:87,
author = "W. H. Fellner",
year = "1987",
title = "Sparse Matrices and the Estimation of Variance
Components by Likelihood Methods",
journal = "Communications in Statistics: Simulation and Computation",
volume = "16",
pages = "439-464",
kwds = "stat, anova, variance components, sparse"
}
@article{felo:74,
author = "T. Fenner and G. Loizou",
year = "1974",
title = "Some New Bounds on the Condition Numbers of Optimally Scaled
Matrices",
journal = "Journal of the {ACM}",
volume = "1",
pages = "514--524",
note = "Cited in \cite{govl:89}.",
kwds = "la, condition, scaling"
}
@inproceedings{fepr:90,
author = "W. Ferzali and J. Proakis",
year = "1990",
title = "Adaptive {SVD} Algorithm with Application to Narrowband Signal
Tracking",
booktitle = "SVD and Signal Processing, {II}",
editor = "R. J. Vaccaro",
pages = "149--160",
publisher = "Elsevier",
address = "Amsterdam",
kwds = "signal processing, svd, updating"
}
-ff- -fg- -fh- -fi-
@article{fipt:62,
author = "M. Fiedler and V. Pt{\'a}k",
year = "1962",
title = "On Matrices with Non-Positive Off-Diagonal Elements
and Positive Principal Minors",
journal = "Czechoslovakian Mathematical Journal",
volume = "12",
pages = "382--400",
kwds = "la, M-matrix"
}
@article{fipt:66,
author = "M. Fiedler and V. Pt{\'a}k",
year = "1962",
title = "Some Results on Matrices of Class {\sf K} and Their
Applications to the Convergence Rate of Iteration Procedures",
journal = "Czechoslovakian Mathematical Journal",
volume = "16",
pages = "260--272",
kwds = "la, nla, M-matrix, iter"
}
@article{fiel:85,
author = "D. A. Field",
year = "1985",
title = "The Focal Point Method for Solving Systems of Linear
Equations",
journal = "Journal of Applied Mathematics and Physics (ZAMP)",
volume = "36",
pages = "24--46",
kwds = "nla, linear system"
}
@unpublished{fibu:91,
author = "R. D. Fierro and J. R. Bunch",
year = "1991",
title = "Collinearity and Total Least Squares",
note = "Manuscript, Department of Mathematics, University of
California, San Diego.",
kwds = "nla, regr, lsq, total least squares"
}
@article{fisc:05,
author = "E. Fischer",
year = "1905",
title = "{\"U}ber quadratische {Formen} mit reelen {Koffizienten}",
journal = "Monatshefte f{\"u}r Mathematik und Physik",
volume = "16",
pages = "234-249",
kwds = "la, eig, geig, symmetric matrix"
}
@article{fius:69,
author = "C. Fischer and R. A. Usmani",
year = "1969",
title = "Properties of Some Tridiagonal Matrices and Their Application to
Boundary Value Problems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "6",
pages = "127--142",
note = "Cited in \cite{govl:89}.",
kwds = "nla, tridiagonal matrix"
}
@book{fish:58,
author = "R. S. Fisher",
year = "1958",
title = "Statistical Methods for Research Workers",
publisher = "Hafner",
address = "New York",
edition = "13th",
kwds = "book, stat"
}
@article{fihe:72,
author = "G. Fix and R. Heiberger",
year = "1972",
title = "An Algorithm for the Ill-Conditioned Generalized
Eigenvalue Problem",
journal = "SIAM Journal on Numerical Analysis",
volume = "9",
pages = "78--88",
kwds = "nla, geig, symmetric matrix, ill-conditioned problem"
}
-fj- -fk- -fl-
@article{flsh:50,
author = "D. A. Flanders and G. Shortly",
year = "1950",
title = "Numerical Determination of Fundemental Modes",
journal = "Journal of Applied Physics",
volume = "21",
pages = "1326--1332",
kwds = "nla, eig, Chebyshev refinement, symmetric matrix, multigrid"
}
@article{flem:90,
author = "H. E. Fleming",
year = "1990",
title = "Equivalence of Regularization and Truncated Iteration
in the Solution of Ill-Posed Image Reconstruction
Problems",
journal = "Linear Algebra and Its Applicaations",
volume = "130",
pages = "133--150",
kwds = "nla, linear system, ill-posed problem, regularization"
}
@article{flre:64,
author = "R. Fletcher and C. M. Reeves",
year = "1964",
title = "Function Minimization by Conjugate Gradients",
journal = "Computer Journal",
volume = "2",
pages = "149--153",
kwds = "nlop, conjugate gradients"
}
@article{flet:65,
author = "R. Fletcher",
year = "1965",
title = "Function Minimization without Evaluating
Derivatives\,---\,a Review",
journal = "Computer Journal",
volume = "8",
pages = "33--41",
kwds = "nlop"
}
@article{flet:68,
author = "R. Fletcher",
year = "1968",
title = "Generalized Inverse Methods for the Best Least Squares
Solution of Systems of Non-Linear Equations",
journal = "Computer Journal",
volume = "10",
pages = "392--399",
kwds = "nlop, ginv, lsq, nllsq"
}
@article{flet:76,
author = "R. Fletcher",
year = "1976",
title = "Factorizing Symmetric Indefinite Matrices",
journal = "Linear Algebra and Its Application",
volume = "14",
pages = "257--272",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lud, symmetric matrix, indefinite system"
}
@book{flet:80,
author = "R. Fletcher",
year = "1980",
title = "Practical Methods of Optimization, Vol. 1, Unconstrained
Optimization",
publisher = "John Wiley",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nlop, lsq, nllsq"
}
@book{flet:81,
author = "R. Fletcher",
year = "1981",
title = "Practical Methods of Optimization, Vol. 2, Constrained
Optimization",
publisher = "John Wiley",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nlop, lsq, constraints, nllsq"
}
@techreport{flet:83,
author = "R. Fletcher",
year = "1983",
title = "Expected Conditioning",
institution = "Department of Mathematics, University of Dundee",
type = "Report",
number = "NA/63",
note = "Includes undated addendum.",
kwds = "la, nla, pert, stochastic analysis, condition"
}
@article{flyn:66,
author = "M. Flynn",
year = "1966",
title = "Very High Speed Computing",
journal = "Proceedings of the IEEE",
volume = "",
pages = "1901-1909",
kwds = "prll, simd, mimd, sisd"
}
-fm- -fn- -fo-
@techreport{forb:89,
author = "A.B. Forbes.",
year = "1989",
title = "Robust Circle and Sphere Fitting by Least Squares",
institution = "National Physical Laboratory, Teddington, UK.",
type = "Technical Report",
number = "NPL DITC 153/89",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@incollection{forb:90,
author = "A.B. Forbes",
year = "1990",
title = "Least Squares Best Fit Geometrical Elements",
pages = "311--319",
booktitle = "Algorithms for Approximation II.",
editor = "J. C. Mason and M. G. Cox",
publisher = "Chapman \& Hall",
address = "London",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{fost:55,
author = "G. E. Forsythe and E. G. Strauss",
year = "1955",
title = "On Best Conditioned Matrices",
journal = "Proceedings of the American Mathematical Society",
volume = "6",
pages = "340--345",
kwds = "la, condition, scaling"
}
@article{fors:57,
author = "G. E. Forsythe",
year = "1957",
title = "Generation and Use of Orthogonal Polynomials for
Data-Fitting with a Digital Computer",
journal = "SIAM Journal",
volume = "5",
pages = "74--88",
note = "Cited in \cite{laha:74}.",
kwds = "nla, lsq, orthogonal polynomial"
}
@article{fors:60,
author = "G. E. Forsythe",
year = "1960",
title = "Crout with Pivoting",
journal = "Communications of the {ACM}",
volume = "3",
pages = "507--508",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, pivoting"
}
@article{fohe:60,
author = "G. E. Forsythe and P. Henrici",
year = "1960",
title = "The Cyclic {Jacobi} Method for Computing the Principle
Values of a Complex Matrix",
journal = "Transaction of the American Mathematical Society",
volume = "94",
pages = "1--23",
kwds = "nla, eig, Jacobi's method, symmetric matrix"
}
@article{fogo:65,
author = "G. E. Forsythe and G. H. Golub",
year = "1965",
title = "On the Stationary Values of a Second Degree Polynomial on the
Unit Sphere",
journal = "SIAM Journal",
volume = "13",
pages = "1050--1068",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, updating"
}
@techreport{fors:66,
author = "G. E. Forsythe",
year = "1966",
title = "How Do You Solve a Quadratic Equation",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS40",
kwds = "nlop, polynomial, rounding error"
}
@techreport{fors:66a,
author = "G. E. Forsythe",
year = "1966",
title = "Today's Computational Methods of Linear Algebra",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS46",
kwds = "nla"
}
@book{fomo:67,
author = "G. Forsythe and C. B. Moler",
year = "1967",
title = "Computer Solution of Linear Algebraic Systems",
publisher = "Prentice-Hall",
address = "Englewood Cliffs , New Jersey",
kwds = "book, math, na, software"
}
@article{fors:70,
author = "G. E. Forsythe",
year = "1970",
title = "Pitfalls in Computation, or Why a Math Book Isn't Enough",
journal = "American Mathematical Monthly",
volume = "77",
pages = "931--957",
kwds = "na, rounding error"
}
@book{fomm:77,
author = "G. E. Forsythe and M. A. Malcolm and C. B. Moler",
year = "1977",
title = "Computer Methods for Mathematical Computations",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, N.J.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, na"
}
@article{fost:86,
author = "L. V. Foster",
year = "1986",
title = "Rank and Nullspace Calculations Using Matrix Decompositions
Without Column Interchanges",
journal = "Linear Algebra and Its Applications",
volume = "74",
pages = "47--71",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, rank determination"
}
@article{fost:90,
author = "L. V. Foster",
year = "1990",
title = "The Probability of Large Diagonal Elements in the
{QR}~Factorization",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "11",
pages = "531--544",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "la, rank determination, qrd"
}
@article{four:84,
author = "R. Fourer",
year = "1984",
title = "Staircase Matrices and Systems",
journal = "{SIAM} Review",
volume = "26",
pages = "1--71",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, staircase matrix"
}
@article{forh:66,
author = "D. W. Fox and W. C. Rheinboldt",
year = "1966",
title = "Computational Methods for Determining Lower Bounds
for Eigenvalues of Operators in {Hilbert} Space",
journal = "SIAM Review",
volume = "8",
pages = "427--462",
kwds = "nla, eig, symmetric matrix"
}
@article{fooh:87,
author= "G. C. Fox and S. W. Otto and A. J. G. Hey",
year = "1987",
title = "Matrix Algorithms on a Hypercube {I}: Matrix
Multiplication",
journal = "Parallel Computing",
volume = "4",
pages = "17-31",
kwds = "nla, prll, hypercube, matrix multiplication"
}
@proceedings{fox:88,
editor = "G. Fox",
year = "1988",
title = "Applications",
series = "The Third Conference on Hypercube Concurrent Computers and
Applications",
volume = "2",
publisher = "{ACM} Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "cs, hypercube, prll"
}
@book{fjlo:88,
author = "G. Fox and M. Johnson and G. Lyzenga and S. Otto and J. Salmon
and D. Walker",
year = "1988",
title = "On Concurrent Processors Vol {I}: General Techniques and Regular
Problems",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, NJ",
note = "Cited in \cite{govl:89}.",
kwds = "book, cs, prll"
}
@book{fox:65,
author = "L. Fox",
year = "1965",
title = "An Introduction to Numerical Linear Algebra",
publisher = "Oxford University Press",
address = "New York",
kwds = "book, nla"
}
@article{fox:87,
author = "L. Fox",
year = "1987",
title = "{James Hardy Wilkinson}",
journal = "Biographical Memoirs of Fellows of the Royal Society",
volume = "33",
pages = "671--708",
kwds = "nla, Wilkinson, history"
}
-fp- -fq- -fr-
@phdthesis{fral:87,
author = "C. Fraley",
year = "1987",
title = "Solution of nonlinear least squares",
school = "Stanford University",
institution = "Department of Computer Science",
number = "STAN-CS-87-1165",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{fral:89,
author = "C. Fraley",
year = "1989",
title = "Computational Behavior of {Gauss-Newton} Methods",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "10",
pages = "515--532",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Gauss-Newton method"
}
@article{fram:64,
author = "J. S. Frame",
year = "1964",
title = "Matrix Functions and Applications, Part {II}",
journal = "{IEEE} Spectrum",
volume = "1",
Month = apr,
pages = "102--108",
note = "Cited in \cite{govl:89}.",
kwds = "la, matrix function"
}
@article{fram:64a,
author = "J. S. Frame",
year = "1964",
title = "Matrix Functions and Applications, Part {IV}",
journal = "{IEEE} Spectrum",
volume = "1",
Month = jun,
pages = "123--131",
note = "Cited in \cite{govl:89}.",
kwds = "la, matrix function"
}
@article{fran:61,
author = "J. G. F. Francis",
year = "1961, 1962",
title = "The {QR}~Transformation, Parts {I} and {II}",
journal = "Computer Journal",
volume = "4",
pages = "265-271, 332-345",
kwds = "nla, eig, QR algorithm"
}
@article{fran:77,
author = "J. W. Frane",
year = "1977",
title = "A Note on Checking Tolerance in Matrix Inversion and Regression",
journal = "Technometrics",
volume = "19",
pages = "513-514",
kwds = "stat, regr, diagnostic, inverse matrix, condition,
rank determination"
}
@article{freu:87,
author = "R. Freund",
year = "1987",
title = "A Note on Two Block {SOR} Methods for Sparse
Least Squares Problems",
journal = "Linear Algebra and Its Applications",
volume = "88/89",
pages = "211--221",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, relaxation"
}
@techreport{frna:91,
author = "R. W. Freund and N. M. Nachtigal",
year = "1991",
title = "{QMR:} a Quasi-Minimal Residual Method for
Non-{Hermitian} Linear systems",
institution = "Interdisciplinary Project Center for Supercomputing,
{Eidgen\"ossische Technische Hochsulle Z\"urich}",
type = "Research Report",
number = "91--05",
kwds = "nla, linear system, nonsymmetric matrix, iter, Krylov sequence"
}
@techreport{frgn:91,
author = "R. W. Freund and M. H. Gutknecht and N. M. Nachtigal",
year = "1991",
title = "An Implementation of the Look-Ahead Lanczos Algorithm
for Non-{Hermitian} Matrices",
institution = "Interdisciplinary Project Center for Supercomputing,
{Eidgen\"ossische Technische Hochsulle Z\"urich}",
type = "Research Report",
number = "91--06",
kwds = "nla, eig, nonsymmetric matrix, Krylov sequence"
}
@article{frie:72,
author = "I. Fried",
year = "1972",
title = "Optimal Gradient Minimization Method Scheme for Finite
Element Eigenproblems",
journal = "Journal of Sound and Vibration",
volume = "20",
pages = "333--342",
kwds = "nla, geig, sparse, finite element, pde, symmetric matrix"
}
@article{frie:72a,
author = "I. Fried",
year = "1972",
title = "Bounds on the Extremal Eigenvalues of the Finite Element
Stiffness and Mass Matrices and Their Spectral Condition
Numbers",
journal = "Journal of Sound and Vibration",
volume = "22",
pages = "407--418",
kwds = "la, gieg, pert, finite element, pde, condition"
}
@article{frie:75,
author = "S. Friedland",
year = "1975",
title = "On Inverse Multiplicative Eigenvalue Problems for Matrices",
journal = "Linear Algebra and its Applications",
volume = "12",
pages = "127--138",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, inverse eigenvalue problem"
}
@article{frie:77,
author = "S. Friedland",
year = "1977",
title = "Inverse Eigenvalue Problems",
journal = "Linear Algebra and its Applications",
volume = "17",
pages = "15--52",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, inverse eigenvalue problem"
}
@article{frno:87,
author = "S. Friedland and J. Nocedal and M. L. Overton",
year = "1987",
title = "The Formulation and Analysis of Numerical Methods for Inverse
Eigenvalue Problems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "24",
pages = "634--667",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, inverse eigenvalue problem"
}
@article{frob:11a,
author = "F. G. Frobenius",
year = "1911",
title = "{\"Uber} den von {L. Bieberbach} gefundenen
{Beweis} eines {Satzes} von {C. Jordan}",
journal = "Sitzungsberichte der K{\"o}niglich Preubischen Akademie der
Wisenschaften zu Berlin",
volume = "3",
pages = "492-501",
note = "In \cite[v. 3, pp. 492--501]{frob:68}.",
kwds = "math, la"
}
@article{frob:11b,
author = "F. G. Frobenius",
year = "1911",
title = "{\"Uber} die unzerlegbaren diskreten {Beweguugsgruppen}",
journal = "Sitzungsberichte der K{\"o}niglich Preusischen Akademie der
Wissenschaften zu Berlin",
volume = "3",
pages = "507-518",
note = "In \cite[v. 3, pp. 507--518]{frob:68}.",
kwds = "math, la"
}
@article{frob:12,
author = "F. G. Frobenius",
year = "1912",
title = " {\"Uber Matrizen aus nicht negativen Elementen}",
journal = "Sitzungsberichte der K{\"o}niglich Preusischen Akademie der
Wissenschaften zu Berlin",
volume = "4",
pages = "456-477",
note = "In \cite[v. 3, pp. 546--567]{frob:68}.",
kwds = "math, la"
}
@book{frob:68,
year = "1968",
author = "F. G. Frobenius",
title = "Ferdinand Georg Frobenius. Gesammelte Abhandlungen
{\rm (J.-P. Serre editor)}",
publisher = "Springer Verlag",
address = "Berlin",
kwds = "book, math, la"
}
@article{frob:65,
author = "C. E. Froberg",
year = "1965",
title = "On Triangularization of Complex Matrices by Two-Dimen\-sional
Unitary Transformations",
journal = "{BIT}",
volume = "5",
pages = "230--234",
note = "Cited in \cite{govl:89}.",
kwds = "nla, complex matrix, triangular matrix"
}
-fs- -ft- -fu-
@article{fuwo:62,
author = "D. R. Fulkerson and P. Wolfe",
year = "1962",
title = "An Algorithm for Scaling Matrices",
journal = "SIAM Review",
volume = "1962",
pages = "142--146",
kwds = "nla, pert, condition, scaling"
}
@book{full:87,
author = "W. A. Fuller",
year = "1987",
title = "Measurement Error Models",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, eriv"
}
@article{fuma:81,
author = "R. E. Funderlic and J. B. Mankin",
year = "1981",
title = "Solution of Homogeneous Systems of Linear Equations
Arising from Compartmental Models",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "375--109",
kwds = "nla, lud, Markov chain, rounding error"
}
@article{fupl:81,
author = "R. E. Funderlic and R. J. Plemmons",
year = "1981",
title = "{LU}~Decomposition of {M}-Matrices by Elimination without
Pivoting",
journal = "Linear Algebra and Its Applications",
volume = "41",
pages = "99--110",
kwds = "nla, lud, Markov chain, M-matrix, rounding error"
}
@article{funp:82,
author = "R. E. Funderlic and M. Neuman and R. J. Plemmons",
year = "1982",
title = "Generalized Diagonally Dominant Matrices",
journal = "Numerische Mathematik",
volume = "40",
pages = "57--70",
note = "Cited in \cite{govl:89}.",
kwds = "nla, diagonal dominance"
}
@article{fupl:84,
author = "R. E. Funderlic and R. J. Plemmons",
year = "1984",
title = "A Combined Direct-Iterative Method for Certain
{M}-Matrix Linear Systems",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "5",
pages = "33--42",
kwds = "nla, Markov chain, lud, linear system, iter, M-matrix"
}
@article{fume:86,
author = "R. E. Funderlic",
year = "1986",
title = "Sensitivity of the Stationary Distribution Vector
for an Ergodic {Markov} Chain",
journal = "Linear Algebra and Its Applications",
volume = "76",
pages = "1--17",
kwds = "nla, eig, pert, Markov chain"
}
@article{fuge:86,
author = "R. E. Funderlic and A. Geist",
year = "1986",
title = "Torus Data Flow for Parallel Computation of Missized Matrix
Problems",
journal = "Linear Algebra and its Applications",
volume = "77",
pages = "149--164",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll"
}
@article{fuwi:74,
author = "G. Furnival and R. Wilson",
year = "1974",
title = "Regression by Leaps and Bounds",
journal = "Technometrics",
volume = "16",
pages = "499-511",
kwds = "stat, regr, updating, variable selection"
}
-fv- -fw- -fx- -fy- -fz-
-ga-
@article{gaza:79,
author = "K. R. Gabriel and S. Zamir",
year = "1979",
title = "Lower Rank Approximation of Matrices by Least Squares with Any
Choice of Weights",
journal = "Technometrics",
volume = "21",
pages = "489-498",
kwds = "stat, nla, svd, matrix approximation, weights"
}
@unpublished{glkh:89,
author = "Pl Gahinet and A. J. Laub and C. Kenny and G. Hewer",
year = "1989",
title = "Sensitivity of the Stable Discrete-Time {Lyapunov} Equation",
note = "Manuscript. Department of Electrical and Computer
Engineering, University of California, Santa Barbara",
kwds = "nla, control, Lyapunov equation, pert, matrix equation"
}
@article{gape:70,
author = "G. Galimberti and V. Pereyra",
year = "1970",
title = "Numerical Differentiation and the Solution of Multidimensional
{V}andermonde Systems",
journal = "Mathematics of Computation",
volume = "24",
pages = "357--364",
note = "Cited in \cite{govl:89}.",
kwds = "nla, numerical differentiation, linear system, Vandermonde matrix"
}
@article{gape:71,
author = "G. Galimberti and V. Pereyra",
year = "1971",
title = "Solving Confluent {V}andermonde Systems of {H}ermite Type",
journal = "Numerische Mathematik",
volume = "18",
pages = "44--60",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, Vandermonde matrix"
}
@article{gajm:87,
author = "K. Gallivan and W. Jalby and U. Meier",
year = "1987",
title = "The Use of {BLAS3} in Linear Algebra on a Parallel Processor with a
Hierarchical Memory",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "8",
pages = "1079--1084",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, memory hierarchy"
}
@techreport{gall:81,
author = "P. P. Gallo",
year = "1981",
title = "Consistency of Regression Estimates When Some Variables are
Subject to Error",
institution = "Institute of Statistics, University of North Carolina at
Chapel Hill",
type = "Mimeo Series",
number = "1328",
kwds = "stat, regr, eriv"
}
@article{galt:1886,
author = "F. Galton",
year = "1886",
title = "Family Likeness in Stature",
journal = "Proceedings of the Royal Society of London",
volume = "40",
pages = "42-63",
kwds = "stat, regr, correlation"
}
@article{galt:1885,
author = "F. Galton",
year = "1885",
title = "Regression towards Mediocrity in Hereditary Stature",
journal = "Journ. Anthrop. Institute",
volume = "246",
pages = "",
kwds = "stat, regr, correlation, regression toward the mean"
}
@article{gand:77,
author = "W. Gander",
year = "1977",
title = "A Machine Independent Algorithm for Computing Percentage
Points of the $\chi^2$-Distribution",
journal = "Journal of Applied Mathematics and Physics (ZAMP)",
volume = "28",
pages = "1133--1136",
kwds = "na, stat, distribution"
}
@article{gand:81,
author = "W. Gander",
year = "1981",
title = "Least Squares with a Quadratic Constraint",
journal = "Numerische Mathematik",
volume = "36",
pages = "291-307",
kwds = "nla, lsq, constraints"
}
@article{gavr:84,
author = "D. Gannon and Van Rosendale, J.",
year = "1984",
title = "On the Impact of Communication Complexity on the Design of
Parallel Numerical Algorithms",
journal = "{IEEE} Transactions on Computers",
volume = "C-33",
pages = "1180--1194",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll, communication"
}
@book{gant:59,
author = "F. R. Gantmacher",
year = "1959",
title = "The Theory of Matrices, Vols. I, II",
publisher = "Chelsea Publishing Company",
address = "New York",
kwds = "book, la"
}
@unpublished{gao:87,
author = "Feng Gao",
year = "1987",
title = "On the Intrinsic Communication Cost of
Parallel {Gaussian} Elimination",
note = "Unpublished Manuscript. Department of Mathematics,
Univeristy of California, Berkeley",
kwds = "nla, lud, prll, communication"
}
@incollection{gbdm:77,
author = "B. S. Garbow and J. M. Boyle and J. J. Dongara and C. B. Moler",
year = "1977",
title = "Matrix Eigensystem Routines-EISPACK Guide Extension",
booktitle = "Lecture Notes in Computer Science",
publisher = "Springer Verlag, New York",
kwds = "nla, eig, eispack, software"
}
@article{gajm:68,
author = "G. R. Garside and P. Jarratt and C. Mack",
year = "1968",
title = "A New Method for Solving Polynomial Equations",
journal = "Computer Journal",
volume = "1968",
pages = "87--90",
kwds = "nlop, polynomial"
}
@techreport{garz:51,
author = "A. de la Garza",
year = "1951",
title = "An Iterative Method for Solving Systems Linear Equations",
institution = "Union Carbide",
adress = "Oak Ridge, Tennessee",
type = "Technical Report",
number = "K-731",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, iter"
}
@book{gaus:1809,
author = "C. F. Gauss",
year = "1809",
title = "Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem
Ambientium",
publisher = "Perthes and Besser",
address = "Hamburg",
kwds = "book, stat, nla, lsq, nlop, nllsq, regr, Gauss-Newton method, lud,
normal equations"
}
@book{gaus:1809a,
author = "C. F. Gauss",
year = "1809",
title = "Theory of the Motion of the Heavenly Bodies Moving about the Sun
in Conic Sections",
publisher = "Dover",
address = "New York (1963)",
note = "C. H. Davis, Trans.",
kwds = "book, stat, nla, lsq, nlop, nllsq, regr, Gauss-Newton method, lud,
normal equations"
}
@incollection{gaus:1810,
author = "C. F. Gauss",
year = "1810",
title = "Disquisitio de Elementis Ellipticis {Palladis}",
booktitle = "Werke, {\rm VI}",
publisher = "K{\"o}niglichen Gesellshaft der Wissenschaften zu
G{\"o}ttingin (1880) ",
pages = "1-24",
kwds = "stat, nla, lsq, lud"
}
@incollection{gaus:1821,
author = "C. F. Gauss",
year = "1821",
title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae,
Pars Prior",
booktitle = "Werke, IV",
publisher = "K{\"o}niglichen Gessellshaft der Wissenschaften zu
G{\"o}ttingin (1880) ",
pages = "1-26",
kwds = "stat, nla, lsq, regr, Gauss-Markov theorem, variance, mean"
}
@incollection{gaus:1823,
author = "C. F. Gauss",
year = "1823",
title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae,
Pars Posterior",
booktitle = "Werke, IV",
publisher = " K{\"o}niglichen Gesellshaft der Wissenschaften zu
G{\"o}ttingin (1880)",
pages = "27-53",
kwds = "stat, nla, lsq, updating"
}
@incollection{gaus:1826,
author = "C. F. Gauss",
year = "1826",
title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae,
Supplementum",
booktitle = "Werke, IV",
publisher = "K{\"o}niglichen Gesselshaft der Wissenschaften zu
G{\"o}ttingin (1880)",
pages = "55-93",
kwds = "math, stat, nla, lsq, geodesy, Gauss-Seidel iteration,
relaxation"
}
@article{gaut:75,
author = "W. Gautschi",
year = "1975",
title = "Norm Estimates for Inverses of {V}andermonde Matrices",
journal = "Numerische Mathematik",
volume = "23",
pages = "337--347",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition, Vandermonde matrix, inverse matrix"
}
@article{gaut:75a,
author = "W. Gautschi",
year = "1975",
title = "Optimally Conditioned {V}andermonde Matrices",
journal = "Numerische Mathematik",
volume = "24",
pages = "1--12",
note = "Cited in \cite{govl:89}.",
kwds = "la, condition, Vandermonde matrix"
}
@article{gaut:83,
author = "W. Gautschi",
year = "1983",
title = "The Condition of {Vandermonde}-like Matrices Involving
Orthogonal Polynomials",
journal = "Linear Algebra and Its Applications",
volume = "52/53",
pages = "293--300",
kwds = "nla, pert, Vandermonde matrix, orthogonal polynomial, condition"
}
@techreport{gay:77,
author = "D. M. Gay",
year = "1977",
title = "Some Convergence Properties of {Broyden's} Method",
institution = "National Bureau of Economic Research",
type = "Working Paper",
number = "175",
kwds = "nlop, quasi-Newton"
}
@techreport{gay:79,
author = "D. M. Gay",
year = "1979",
title = "On Solving Robust and Generalized Linear Regression Problems",
institution = "Mathematics Research Center, University of Wisconsin",
type = "MRC Technical Summary",
number = "2000",
kwds = "math, stat, regr, nla, robust estimation,
generalized linear model"
}
@article{gay:83,
author = "D. M. Gay",
year = "1983",
title = "Algorithm 611. Subroutines for Unconstrained Minimization Using
a Model/Trust-region Approach",
journal = " ACM Transactions on Mathematical Software",
volume = "9",
pages = "503--524",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@inproceedings{gay:84,
author = "D. M. Gay",
year = "1984",
title = "A Trust-region Approach to Linearly Constrained Optimization",
pages = "72--105",
booktitle = "In Proceedings of the 1983 Dundee Conference on Numerical
Analysis",
editor = "D.F. Griffiths",
publisher = "Springer Verlag",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
@article{gay:91,
author = "D. M. Gay",
year = "1991",
title = "Massive Memory Buys Little Speed for Complete, In-Core
Sparse Cholesky Factorization on Some Scalar Computers",
journal = "Linear Algebra and Its Applications",
volume = "152",
pages = "291--314",
kwds = "nla, lud, Cholesky decomposition, sparse"
}
-gb- -gc- -gd- -ge-
@techreport{gehe:85,
author = "G. A. Geist and M. T. Heath",
year = "1985",
title = "Parallel {C}holesky Factorization on a Hypercube Multiprocessor",
number = "ORNL 6190",
institution = "Oak Ridge Laboratory",
address = "Oak Ridge, TN",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, Cholesky decomposition, hypercube"
}
@incollection{gehe:86,
author = "G. A. Geist and M. T. Heath",
year = "1986",
title = "Matrix Factorization on a Hypercube",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = "{SIAM} Publications",
pages = "161--180",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, prll, hypercube"
}
@inproceedings{gwdf:88,
author = "G. A. Geist and R. C. Ward and G. J. Davis and R. E. Funderlic",
year = "1988",
title = "Finding Eigenvalues and Eigenvectors of Unsymmetric Matrices Using
a Hypercube Multiprocessor",
booktitle = "The Third Conference on Hypercube Concurrent Computers and
Applications, Vol. {II}, Applications",
editor = "G. Fox",
publisher = "{ACM} Press",
address = "New York",
pages = "1577--1582",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, eig, hypercube"
}
@techreport{gelw:89,
author = "G. A. Geist and A. Lu and E. L. Wachspress",
year = "1989",
title = "Stabilized Gaussian Reduction of an Arbitrary Matrix
to Tridiagonal Form",
institution = "Mathemaical Sciences Section, Oak Ridge National
Laboratory",
type = "Technical Report",
number = "ORNL/TM-11089",
kwds = "nla, eig, tridiagonal matrix"
}
@article{gema:80,
author = "A. Geman",
year = "1980",
title = "A Limit Theorm for the Norm of Random Matrices",
journal = "The Annals of Probability",
volume = "8",
pages = "252-261",
kwds = "stat, la, norm, random matrix"
}
@article{gent:73,
author = "W. M. Gentleman",
year = "1973",
title = "Least Squares Computations by {Givens} Transformations
Without Square Roots",
journal = "J. Inst. Maths. Applics.",
volume = "12",
pages = "329--336",
kwds = "nla, lsq, qrd, fast algorithm, plane rotation"
}
@article{gent:75,
author = "W. M. Gentleman",
year = "1975",
title = "Error Analysis of {QR} Decompositions by {Givens} Transformations",
journal = "Linear Algebra and Its Applications",
volume = "10",
pages = "189--197",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, qrd, plane rotation"
}
@inproceedings{geku:82,
author = "W. M. Gentleman and H. T. Kung",
year = "1982",
title = "Matrix Triangularization by Systolic Arrays",
booktitle = "{SPIE} Proceedings",
volume = "298",
pages = "19--26",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, systolic, prll, plane rotation"
}
@inproceedings{gent:76,
author = "W. M. Gentleman",
year = "1976",
title = "Row Elimination for Solving Sparse Linear Systems and
Least Squares Problems",
booktitle = "In Proceedings the 6th Dundee Conference on
Numerical Analysis",
publisher = "Springer Verlag",
pages = "122--133",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse, linear system"
}
@techreport{gent:85,
author = "W. M. Gentleman",
year = "1985",
title = "Using the Harmony Operating System",
institution = "Natonal Research Council of Canada",
type = "Technical Report",
number = "ERB-966",
kwds = "prll, message passing, operating system"
}
@inproceedings{geor:72,
author = "J. A. George",
year = "1972",
title = "Block Eliminations on Finite Element Systems of
Equations",
booktitle = "Sparse Matrices and their Applications",
editor = "D. J. Rose and R. A. Willoughby",
pages = "101--114",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, finite element, sparse, linear system"
}
@article{geor:73,
author = "J. A. George",
year = "1973",
title = "Nested Dissection of a Regular Finite Element Mesh",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "10",
pages = "345--363",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, nested dissection, sparse, finite element"
}
@article{geor:74,
author = "J. A. George",
year = "1974",
title = "On Block Elimination for Sparse Linear Systems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "585--603",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, lud, sparse, linear system"
}
@article{gepv:78,
author = "J. A. George and W.G. Poole and R.G. Voigt",
year = "1978",
title = "Incomplete Nested Dissection for Solving $n$ by $n$ Grid Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "90--112",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, nested dissection, incomplete factorization"
}
@article{gehe:80,
author = "A. George and M. T. Heath",
year = "1980",
title = "Solution of Sparse Linear Least Squares Problems
Using {Givens} Rotations",
journal = "Linear Algebra and Its Application",
volume = "34",
pages = "69--83",
kwds = "nla, sparse, lsq, qrd, plane rotation"
}
@book{geli:81,
author = "J. A. George and J. W. H. Liu",
year = "1981",
title = "Computer Solution of Large Sparse Positive Definite Systems",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, NJ.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, positive definite matrix, sparse, linear system"
}
@article{gehp:81,
author = "J. A. George and M. T. Heath and R. J. Plemmons",
year = "1981",
title = "Solution of Large-Scale Sparse Least Squares Problems
Using Auliliary Storage",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "416--429",
kwds = "nla, lsq, sparse, qrd, memory hierarchy"
}
@techreport{gehn:81,
author = "A. George and M. T. Heath and E. Ng",
year = "1981",
title = "A Comparison of Some Methods for Solving Sparse Linear Least
Squares Problems",
institution = "Computer Science Division, Oak Ridge National Laboratory",
number = "87",
kwds = "nla, lsq, sparse"
}
@article{geng:83,
author = "J. A. George and E. Ng",
year = "1981",
title = "On Row and Column Orderings for Sparse Least Squares Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "20",
pages = "326--344",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, qrd, plane rotation"
}
@article{gehn:83,
author = "J. A. George and M. T. Heath and E. Ng",
year = "1983",
title = "A Comparison of Some Methods for Solving Sparse Linear Least
Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "4",
pages = "177--187",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{geln:84,
author = "J. A. George and J. H. W. Liu and E. Ng",
year = "1984",
title = "Row Ordering Schemes for Sparse {Givens} Transformations,
I. Bipartite Graph Model",
journal = "Linear Algebra and Its Applcations",
volume = "81",
pages = "55--81",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, sparse, plane rotation"
}
@techreport{geng:84,
author = "J. A. George and E. Ng",
year = "1984",
title = "{SPARSPAK}: Waterloo Sparse Matrix Package User's Guide for
{SPARSPAK-B}",
institution = "Dept. of Computer Science, University of Waterloo",
type = "Research Report",
number = "CS-84-37",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, sparse"
}
@article{gehl:86,
author = "A. George and M. T. Heath and J. Liu",
year = "1986",
title = "Parallel {Cholesky} Factorization on a Shared-Memory
Multiprocessor",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "165--187",
kwds = "nla, prll, lud, Cholesky decomposition, shared memory"
}
@article{geng:87,
author = "J. A. George and E. Ng",
year = "1987",
title = "Symbolic Factorization for Sparse Gaussian Elimination with
Partial Pivoting",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "877--898",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, lud"
}
@techreport{gech:87,
author = "Alan George and Eleanor Chu",
year = "1987",
title = "{Gaussian} Elimination with Partial Pivoting
and Load Balancing on a Multiprocessor",
institution = "Mathematical Sciences Section, Oak Ridge
National Laboratory",
number = "ORNL/TM-10323",
kwds = "nla, prll, lud, load balancing, pivoting"
}
@article{geli:87,
author = "J. A. George and J. H. W. Liu",
year = "1987",
title = "{Householder} Reflections versus {Givens} Rotations in Sparse
Orthogonal Decomposition",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "223--238",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, qrd, sparse"
}
@article{ghln:88,
author = "A. George and M. T. Heath and J. Liu and E. Ng",
year = "1988",
title = "Sparse {Cholesky} Factorization on a Local-Memory
Multiprocessor",
journal = "SIAM Journal on Scientific and Statiscal Computing",
volume = "9",
pages = "327-340",
kwds = "nla, prll, lud, sparse, Cholesky decomposition,
sparse, message passing"
}
@article{geli:89,
author = "J. A. George and J. H. W. Liu",
year = "1989",
title = "The Evolution of the Minimum Degree Ordering Algorithm",
journal = "SIAM Review",
volume = "31",
pages = "1--19",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lud, sparse, history"
}
@article{gera:76,
author = "V. J. Geraci",
year = "1976",
title = "Identification of Simultaneous Equation Models
with Measurement Error",
journal = "Journal of Econometrics",
volume = "4",
pages = "263--283",
kwds = "stat, eriv, regr"
}
@article{gera:77,
author = "V. J. Geraci",
year = "1977",
title = "Estimation of Simultaneous Equation Models with
Measurement Error",
journal = "Econometrica",
volume = "45",
pages = "1243--1255",
kwds = "stat, regr, eriv"
}
@article{gera:71,
author = "M. Geradin",
year = "1977",
title = "The Computational Efficiency of a New Minimization
Algorithm for Eigenvalue Analysis",
journal = "Journal of Sound and Vibration",
volume = "19",
pages = "319--331",
kwds = "nla, eig, sparse"
}
@article{gera:88,
author = "A. Gerasoulis",
year = "1988",
title = "A Fast Algorithm for the Multiplication of Generalized
{Hilbert} Matrices with Vectors",
journal = "Mathematics of Computation",
volume = "50",
pages = "179-188",
kwds = "nla, Hilbert matrix, fast algorithm, matrix-vector product"
}
@article{gers:31,
author = "S. A. Gerschgorin",
year = "1931",
title = " {\"Uber die Abgrenzung der Eigenwerte einer Matrix}",
journal = "Izvestia Akademii Nauk SSSR, Mathematics and Natural
Sciences",
volume = "6",
pages = "749--754",
kwds = "la, eig, pert, Gerschgorin's theorem"
}
-gf- -gg- -gh-
@article{ghez:85,
author = "Carlo Ghezzi",
year = "1985",
title = "Concurrency in Programming Languages: A Survey",
journal = "Parallel Computing",
volume = "2",
pages = "224-241",
kwds = "prll"
}
-gi-
@article{gipo:74,
author = "N. E. Gibbs and W. G. Poole, Jr",
year = "1974",
title = "Tridiagonalization by Permutations",
journal = "Communications of the {ACM}",
volume = "17",
pages = "20--24",
note = "Cited in \cite{govl:89}.",
kwds = "nla, tridiagonal matrix, permutation matrix"
}
@article{gips:76,
Author = "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer",
year = "1976",
title = "A Comparison of Several Bandwidth and
Profile Reduction Algorithms",
journal = "{ACM} Transactions on Mathematical Software",
volume = "2",
pages = "322--330",
note = "Cited in \cite{govl:89}.",
kwds = "nla, band matrix, band reduction, profile reduction, sparse"
}
@article{gips:76a,
author = "N. E. Gibbs and W. G. Poole and P. K. Stockmeyer",
year = "1976",
title = "An Algorithm for Reducing the Bandwidth and Profile of a Sparse
Matrix",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "13",
pages = "236--250",
note = "Cited in \cite{govl:89}.",
kwds = "nla, band matrix, band reduction, profile reduction, sparse"
}
@article{gims:92,
author = "J. R. Gilbert and C. Moler and R. Screiber",
year = "1992",
title = "Sparse Matrices in {MATLAB}: Design and Implementation",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages ="333--356",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse"
}
@article{ggms:74,
author = "P. E. Gill and G. H. Golub and W. Murray and M. A. Saunders",
year = "1974",
title = "Methods of Modifying Matrix Factorizations",
journal = "Mathematics of Computation",
volume = "28",
pages = "505-535",
kwds = "math, nla, qrd, lud, updating"
}
@article{gims:75,
author = "P. E. Gill and W. Murray and M. A. Saunders",
year = "1975",
title = "Methods for Computing and Modifying the {$LDU$}~Factors
of a Matrix",
journal = "Mathematics of Computation",
volume = "29",
pages = "1051--1077",
kwds = "nla, lud, updating, sparse"
}
@inproceedings{gimu:76,
author = "P.E. Gill and W. Murray",
year = "1976",
title = "Nonlinear Least Squares and Nonlinearly Constrained Optimization",
booktitle = "In Proceedings Dundee Conference on Numerical Analysis 1975",
publisher = "Springer Verlag",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
@inproceedings{gimu:76a,
author = "P.E. Gill and W. Murray",
year = "1976",
title = "The Orthogonal Factorization of a Large Sparse Matrix",
pages = "201--212",
booktitle = "Sparse Matrix Computations",
editor = "J. R. Bunch and D. J. Rose",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, qrd"
}
@article{gimu:78,
author = "P.E. Gill and W. Murray",
year = "1978",
title = "Algorithms for the Solution of the Nonlinear Least
Squares Problem",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "977--992",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@book{gimw:81,
author = "P.E. Gill and W. Murray and M.H. Wright",
year = "1981",
title = "Practical Optimization",
publisher = "Academic Press",
address = "London and New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nlop"
}
@article{gmss:85,
author = "P. Gill and W. Murray and M. Saunders and G. W. Stewart
and M. Wright",
year = "1985",
title = "Properties of a Representation of a Basis
for the Null Space",
journal = "Mathematical Programming",
volume = "33",
pages = "172--186",
kwds = "nla, nlop"
}
@inproceedings{gims:90,
author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright",
year = "1990",
title = "A {Schur}-complement Method for Sparse Quadratic Programming",
booktitle = "Reliable Numerical Computation",
editor = "M.G. Cox and S. Hammarling",
pages = "113--138",
publisher = "Clarendon Press",
address = "Oxford",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop"
}
@incollection{gins:71,
author = "T. Ginsburg",
year = "1971",
title = "The Conjugate Gradient Method",
booktitle = "Handbook for Automatic Computation Vol. 2: Linear Algebra",
editor = "J. H. Wilkinson and C. Reinsch",
publisher = "Springer",
address = "New York",
kwds = "nla, linear system, conjugate gradients"
}
@techreport{give:54,
author = "W. Givens",
year = "1954",
title = "Numerical Computation of the Characteristic Values of a Real
Matrix",
institution = "Oak Ridge National Laboratory",
number = "1574",
kwds = "nla, eig, rounding error, plane rotation, symmetric matrix"
}
@article{give:58,
author = "W. Givens",
year = "1958",
title = "Computation of Plane Unitary Rotations Transforming a General
Matrix to Triangular Form",
journal = " SIAM Journal on Applied Mathematics",
volume = "6",
pages = "26--50",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, plane rotation"
}
-gj- -gk- -gl- -gm- -gn- -go-
@book{gokr:69,
author = "I. C. Gohberg and M. G. Krein",
year = "1969",
title = "Introduction to the Theory of Linear Nonselfadjoint Operators",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
kwds = "book, svd, functional analysis"
}
@article{golr:78,
author = "I. Gohberg and P. Lancaster and L. Rodman",
year = "1978",
title = "Spectral Analysis of Matrix Polynomials---{I}. {Canonical}
Forms and Divisors",
journal = "Linear Algebra and Its Applications",
volume = "20",
pages = "1--44",
kwds = "la, geig, matrix polynomial"
}
@article{golr:78a,
author = "I. Gohberg and P. Lancaster and L. Rodman",
year = "1978",
title = "Spectral Analysis of Matrix Polynomials---{II}. {The}
Resolvent Form and Spectral Divisors",
journal = "Linear Algebra and Its Applications",
volume = "21",
pages = "65--88",
kwds = "la, geig, matrix polynomial"
}
@book{golr:82,
author = "I. Gohberg and P. Lancaster and L. Rodman",
year = "1982",
title = "Matrix Polynomials",
publisher = "Academic Press",
address = "New York",
kwds = "book, la, geig, matrix pencil, matrix polynomial"
}
@book{golr:86,
author = "I. Gohberg and P. Lancaster and L. Rodman",
year = "1986",
title = "Invariant Subspaces of Matrices with Applications",
publisher = "John Wiley",
address = "New York",
kwds = "book, la, pert, geig, invariant subspace"
}
@book{gold:68,
author = "A. S. Goldberger",
year = "1968",
title = "Topics in Regression Analysis",
publisher = "Macmillan",
address = "New York",
kwds = "book, stat, regr"
}
@article{gold:72,
author = "D. Goldfarb",
year = "1972",
title = "Modification Methods for Inverting Matrices and Solving
Systems of Linear Algebraic Equations",
journal = "Mathematics of Computation",
volume = "26",
pages = "829--852",
kwds = "nla, nlop, inverse matrix, linear system, updating"
}
@article{goze:64,
author = "A. J. Goldman and M. Zelen",
year = "1964",
title = "Weak Generalized Inverses and Minimum Variance Linear
Unbiased Estimation",
journal = "Journal of Research of the National Bureau of Standards---B.
Mathematics and Mathematical Physics",
volume = "68B",
pages = "151--172",
kwds = "stat, ginv, regr, Gauss-Markov theorem"
}
@article{gosm:74,
author = "M. Goldstein and A. F. M. Smith",
year = "1974",
title = "Ridge-type Estimators for Regression Analysis",
journal = "??????????",
volume = "??",
pages = "284--291",
kwds = "stat, regr, ridge regression"
}
@article{govn:51,
author = "H. H. Goldstine and von Neumann, J.",
year = "1951",
title = "Numerical Inverting of Matrices of High Order, {II}",
journal = "Proceedings of the American Mathematical Society",
volume = "2",
pages = "188-202",
kwds = "nla, inverse matrix, random matrix"
}
@article{goho:59,
author = "H. H. Goldstine and L. P. Horowitz",
year = "1959",
title = "A Procedure for the Diagonalization of Normal Matrices",
journal = "Journal of the {ACM}",
volume = "6",
pages = "176--195",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, normal matrix"
}
@article{gova:61,
author = "G. H. Golub and R. S. Varga",
year = "1961",
title = "{C}hebychev Semi-Iterative Methods, Successive Over-Relaxation
Iterative Methods, and Second-Order {R}ichardson Iterative Methods,
Parts {I} and {II}",
journal = "Numerische Mathematik",
volume = "3",
pages = "147--156, 157--168",
note = "Cited in \cite{govl:89}.",
kwds = "nla, relaxation, iter, semi-iterative method, Richardson's method"
}
@article{goka:65,
author = "G. H. Golub and W. Kahan",
year = "1965",
title = "Calculating the Singular Values and Pseudo-Inverse of a Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "2",
pages = "205-224",
kwds = "nla, svd, ginv"
}
@inproceedings{gowi:65,
author = "G. H. Golub and J. H. Wilkinson",
year = "1965",
title = "Iterative Refinement of Least Square Solution",
booktitle = "Proceedings of the IFIP Congress 65",
editor = "",
pages = "606--607",
publisher = "",
address = "",
kwds = "nla, lsq, iterative refinement"
}
@article{golu:65,
author = "G. H. Golub",
year = "1965",
title = "Numerical Methods for Solving Least Squares Problems",
journal = "Numerische Mathematik",
volume = "7",
pages = "206-216",
kwds = "nla, lsq, qrd, Householder transformation, updating"
}
@article{gowi:66,
author = "G. H. Golub and J. H. Wilkinson",
year = "1966",
title = "Note on the Iterative Refinement of Least Squares Solution",
journal = "Numerische Mathematik",
volume = "9",
pages = "139-148",
kwds = "la, nla, lsq, pert, condition, iterative refinement"
}
@article{golu:68,
author = "G. H. Golub",
year = "1968",
title = "Least Squares, Singular Values, and Matrix Approximations",
journal = "Aplicace Mathematicky",
volume = "13",
pages = "44--51",
kwds = "nla, lsq, regr, svd, Schmidt-Mirsky theorem"
}
@techreport{golu:69,
author = "G. H. Golub",
year = "1969",
title = "Matrix Decompositions and Statistical Calculations",
institution = "Computer Science Department, Stanford University",
number = "124",
kwds = "stat, nla, lsq, qrd, svd"
}
@article{gowe:69,
author = "G. H. Golub and J. H. Welsch",
year = "1969",
title = "Calculation of {G}auss Quadrature Rules",
journal = "Mathematics of Computation",
volume = "23",
pages = "221--230",
note = "Cited in \cite{govl:89}.",
kwds = "na, Gaussian quadrature"
}
@techreport{goun:69,
author = "G. H. Golub and R. Underwood",
year = "1969",
title = "Stationary Values of the Ratio of Quadratic Forms Subject to
Linear Constraints",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS-142",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, geig, regularization"
}
@inproceedings{golu:69a,
author = "G. H. Golub",
year = "1969",
title = "Matrix Decompositions and Statistical Computation",
pages = "365--397",
booktitle = "Statistical Computation",
editor = "R.C. Milton and J. A. Nelder",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, nla, lsq, qrd, svd"
}
@article{gore:70,
author = "G. H. Golub and C. Reinsch",
year = "1970",
title = "Singular Value Decomposition and Least Squares Solution",
journal = "Numerische Mathematik",
volume = "14",
pages = "403--420",
note = "Also in \cite[pp.134--151]{wire:71}.",
kwds = "nla, svd, lsq, rank determination, regularization, software"
}
@inproceedings{gosa:70,
author = "G. H. Golub and M. A. Saunders",
year = "1970",
title = "Linear Least Squares and Quadratic Programming",
pages = "229--256",
booktitle = "Integer and Nonlinear Programming",
editor = "J. Abadie",
publisher = "North-Holland Publ. Co.",
address = "Amsterdam-London",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, qrd, lsq, quadratic programming"
}
@article{goun:70,
author = "G. H. Golub and R. Underwood",
year = "1970",
title = "Stationary Values of the Ratio of Quadratic Forms Subject to
Linear Constraints",
journal = "Journal of Mathematical Physics",
volume = "21",
pages = "318--326",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, constraints, symmetric matrix"
}
@techreport{gouw:72,
author = "G. H. Golub and R. Underwood and J. H. Wilkinson",
year = "1972",
title = "The {L}anczos Algorithm for the Symmetric
{$Ax = \lambda Bx$} Problem",
number = "STAN-CS-72-270",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, Lanczos algorithm"
}
@article{golu:73,
author = "G. H. Golub",
year = "1973",
title = "Some Modified Matrix Eigenvalue Problems",
journal = "SIAM Review",
volume = "15",
pages = "318--344",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, eig, updating"
}
@article{gost:73,
author = "G. H. Golub and G. P. Styan",
year = "1973",
title = "Numerical Computations for Univariate Linear Models",
journal = "J. Stat. Comput. Simul.",
volume = "2",
pages = "253-274",
kwds = "stat, nla, regr, lsq, qrd"
}
@article{gope:73,
author = "G. H. Golub and V. Pereyra",
year = "1973",
title = "The Differentiation of Pseudoinverses and Nonlinear
Least Squares Problems Whose Variables Separate",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "413--432",
kwds = "la, nlop, nllsq, pert, ginv, projection, lsq, matrix derivative"
}
@incollection{golu:74,
author = "G. H. Golub",
year = "1974",
title = "Some Uses of the {L}anczos Algorithm in Numerical Linear Algebra",
booktitle = "Topics in Numerical Analysis",
editor = "J. J. H. Miller",
publisher = "Academic Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm"
}
@article{gova:74,
author = "G. H. Golub and J. M. Varah",
year = "1974",
title = "On a Characterization of the Best {$L_{2}$}-Scaling of a Matrix",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "472--479",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition, scaling"
}
@techreport{goks:76,
author = "G. H. Golub and V. Klema and G. W. Stewart",
year = "1976",
title = "Rank Degeneracy and Least Squares Problems",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "TR-456",
kwds = "nla, svd, qrd, condition estimation, rank determination, pert"
}
@article{gowi:76,
author = "G. H. Golub and J. H. Wilkinson",
year = "1976",
title = "Ill-Conditioned Eigensystems and the Computation
of the {Jordan} Canonical Form",
journal = "SIAM Review",
volume = "18",
pages = "578--619",
kwds = "nla, eig, Jordan form, condition, pert, ill-conditioned problem"
}
@inproceedings{gope:76,
author = "G. H. Golub and V. Pereyra",
year = "1976",
title = "Differentiation of Pseudoinverses, Separable
Nonlinear Least Squares Problems and Other Tales",
booktitle = "Generalized Inverses and Applications",
editor = "M. Z. Nashed",
pages = "303--324",
publisher = "Academic Press",
address = "New York",
kwds = "la, nlop, nllsq, pert, ginv, projection, lsq, matrix derivative"
}
@incollection{goun:77,
author = "G. H. Golub and R. Underwood",
year = "1977",
title = "The Block {L}anczos Method for Computing Eigenvalues",
booktitle = "Mathematical Software {III}",
editor = "J. Rice",
publisher = "Academic Press",
address = "New York",
pages = "364--377",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, Lanczos algorithm, eig"
}
@article{govl:79,
author = "G. H. Golub and Van Loan, C. F.",
year = "1979",
title = "Unsymmetric Positive Definite Linear Systems",
journal = "Linear Algebra and its Applications",
volume = "28",
pages = "85--98",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, positive definite matrix, nonsymmetric matrix"
}
@article{gonv:79,
author = "G. H. Golub and S. Nash and Van Loan, C.",
year = "1979",
title = "{Hessenberg--Schur} Method for the Problem {$AX+XB=C$}",
journal = "IEEE Transactions on Automatic Control",
volume = "AC-24",
pages = "909--913",
kwds = "nla, Sylvester equation, Hessenberg matrix, Schur form,
Lyapunov equation, matrix equation"
}
@article{gohw:79,
author = "G. H. Golub and M. T. Heath and G. Wahba",
year = "1979",
title = "Generalized Cross-Validation as a Method for Choosing a Good
Ridge Parameter",
journal = "Technometrics",
volume = "21",
pages = "215--223",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, stat, ridge regression, cross validation, regularization"
}
@inproceedings{govl:79,
author = "G. H. Golub and Van Loan, C. F.",
year = "1979",
title = "Total least squares",
pages = "69--76",
booktitle = "Smoothing Techniques for Curve Estimation",
editor = "T. Gasser and M. Rosenblatt",
publisher = "Springer-Verlag",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, total least squares"
}
@article{govl:80,
author = "G. H. Golub and Van Loan, C. F.",
year = "1980",
title = "An Analysis of the Total Least Squares Problem",
journal = "SIAM Journal on Numerical Analysis",
volume = "17",
pages = "883-893",
kwds = "math, nla, lsq, svd, eriv, total least squares"
}
@article{gopl:80,
author = "G. H. Golub and R. J. Plemmons",
year = "1980",
title = "Large-Scale Geodetic Least-Squares Adjustment by Dissection
and Orthogonal Decomposition",
journal = "Linear Algebra and Its Applications",
volume = "34",
pages = "3--27",
kwds = "nla, lsq, sparse, geodesy, qrd"
}
@article{golo:81,
author = "G. H. Golub and F. T. Luk and M.L. Overton",
year = "1981",
title = "A Block {Lanczos} Method for Computing the Singular Values and
Corresponding Singular Vectors of a Matrix",
journal = "ACM Transactins on Mathematical Software",
volume = "7",
pages = "149--169",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, Lanczos algorithm"
}
@article{gota:81,
author = "G. H. Golub and W. P. Tang",
year = "1981",
title = "The Block Decomposition of a {V}andermonde Matrix and Its
Applications",
journal = "{BIT}",
volume = "21",
pages = "505--517",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, Vandermonde matrix"
}
@article{gona:82,
author = "G. H. Golub and S. G. Nash",
year = "1982",
title = " Nonorthogonal Analysis of Variance using a Generalized
Conjugate-Gradient Algorithm",
journal = "Journal of the American Statistical Association",
volume = "77",
pages = "109--116",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, anova, conjugate gradients"
}
@book{govl:83,
author = "G. H. Golub and Van Loan, C. F.",
year = "1983",
title = "Matrix Computations",
publisher = "Johns Hopkins University Press",
address = "Baltimore, Maryland",
kwds = "book, nla"
}
@book{gome:83,
author = "G. H. Golub and G. Meurant",
year = "1983",
title = "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes
Lin{\'e}aires",
series = "Collection de la Direction des Etudes et Recherches de
l'Electricit\'e de France",
volume = "49",
publisher = "Eyolles",
address = "Paris",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, linear system, sparse"
}
@article{gome:85,
author = "G. H. Golub and C. D. Meyer",
year = "1985",
title = "Using the {QR}~Factorization and Group Inversion
to Compute, Differentiate, and Estimate the
Sensitivity of Stationary Probabilities for
{Markov} Chains",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "7",
pages = "273-281",
kwds = "nla, qrd, Markov chain"
}
@article{gomt:86,
author = "G. H. Golub and P. Manneback and P. Toint",
year = "1986",
title = "A Comparison Between some Direct and Iterative Methods for
Large Scale Geodetic Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "799--816",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, lsq, geodesy, conjugate gradients, nested dissection,
iter"
}
@article{gome:86,
author = "G. H. Golub and C. D. Meyer",
year = "1986",
title = "Using the {QR} Factorization and Group Inversion to Compute,
Differentiate, and estimate the Sensitivity of Stationary
Probabilities for {M}arkov Chains",
journal = "{SIAM} Journal on Algebraic and Discrete Methods",
volume = "7",
pages = "273--281",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, ginv, Markov chain, eig"
}
@article{gohs:87,
author = "G. H. Golub and A. Hoffman and G. W. Stewart",
year = "1987",
title = "A Generalization of the {Eckart-Young} Matrix
Approximation Theorem",
journal = "Linear Algebra and Its Applications",
volume = "88/89",
pages = "317--327",
kwds = "la, matrix approximation"
}
@inproceedings{gops:88,
author = "G. H. Golub and R. J. Plemmons and A. Sameh",
year = "1988",
title = "Parallel Block Schemes for Large-Scale Least-Squares Computations",
pages = "171-179",
booktitle = "High-Speed Computing, Scientific Applications and Algorithm
Design",
publisher = "University of Illinois Press",
address = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, iter"
}
@article{goov:88,
author = "G. H. Golub and M. Overton",
year = "1988",
title = "The Convergence of Inexact {C}hebychev and {R}ichardson Iterative
Methods for Solving Linear Systems",
journal = "Numerische Mathematik",
volume = "53",
pages = "571--594",
note = "Cited in \cite{govl:89}.",
kwds = "nla, iter, linear system"
}
@book{govl:89,
author = "G. H. Golub and Van Loan, C. F.",
year = "1989",
title = "Matrix Computations",
edition = "2nd",
publisher = "Johns Hopkins University Press",
address = "Baltimore, Maryland",
kwds = "book, math, na, nla"
}
@article{govm:91,
author = "G. H. Golub and von Matt, U.",
year = "1991",
title = "Quadratically Constrained Least Squares and
Quadratic Problems",
journal = "Numerische Mathematik",
volume = "59",
pages = "561--580",
kwds = "nla, nlop, nllsq, lsq, constraints"
}
@article{good:69,
author = "I. J. Good",
year = "1969",
title = "Some Applications of the Singular Decomposition
of a Matrix",
journal = "Technometrics",
volume = "11",
pages = "823--831",
kwds = "stat, svd"
}
@article{good:79,
author = "J. H. Goodnight",
year = "1979",
title = "A Tutorial on the SWEEP Operator",
journal = "American Statistician",
volume = "33",
pages = "149-158",
kwds = "stat, regr, inverse matrix, sweep operator, updating"
}
@article{good:80,
author = "J. H. Goodnight",
year = "1980",
title = "Tests of Hypotheses in Fixed Effects Linear Models",
journal = "Communications in Statistics",
volume = "A9",
pages = "167-180",
kwds = "stat, regr, hypothesis testing"
}
@article{goea:83,
author = "A. Gottlieb and R. Grishman and C. P. Kruskal and
K. P. McAuliffe and L. Rudolph and M. Snir",
year = "1983",
title = "The {NYU} Ultracomputer---Designing an {MIMD} Shared
Memory Parallel Computer",
journal = "IEEE Transactions on Computing",
volume = "c32",
pages = "175-189",
kwds = "prll, shared memory, communication, ultracomputer"
}
@techreport{goul:90,
author = "N. Gould",
year = "1990",
title = "On Growth in {Gaussian} Elimination with Complete
Pivoting",
institution = "Rutherford Appleton Laboratory",
type = "Technical Report",
number = "RAL-90-075",
kwds = "nla, lud, pivoting"
}
@article{gour:70,
author = "A. R. Gourlay",
year = "1970",
title = "Generalization of Elementary {H}ermitian Matrices",
journal = "The Computer Journal",
volume = "13",
pages = "411--412",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Householder transformation"
}
@article{gova:91,
author = "W. Govaerts",
year = "1991",
title = "Stable Solvers and Block Elimination for Bordered
Systems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "469--483",
kwds = "nla, lud, block algorithm, iterative refinement"
}
-gp- -gq- -gr-
@article{grad:70,
author = "J. Grad",
year = "1970?",
title = "Matrix Balancing",
journal = "Computer Journal",
volume = "14",
pages = "280--284",
kwds = "nla, scaling"
}
@article{grho:66,
author = "W. B. Gragg and A. S. Householder",
year = "1968",
title = "On a Theorem of {Koenig}",
journal = "Numerische Mathematik",
volume = "8",
pages = "465--468",
kwds = "nlop, Koenig's theorem"
}
@article{grag:68,
author = "W. B. Gragg",
year = "1968",
title = "Truncation Error Bounds for $g$-Fractions",
journal = "Numerische Mathematik",
volume = "11",
pages = "370--379",
kwds = "na, continued fraction"
}
@article{gragg:70,
author = "W. B. Gragg",
year = "1970",
title = "Truncation Error Bounds for $\pi$-Fractions",
journal = "Bulletin of the American Mathematical Society",
volume = "76",
pages = "1091--1094",
kwds = "na, continued fraction"
}
@article{gragg:72,
author = "W. B. Gragg",
year = "1972",
title = "The {Pad\'e} Table and Its Relation to Certain Algorithms
of Numerical Analysis",
journal = "SIAM Review",
volume = "14",
pages = "1--62",
kwds = "na, Pade table, continued fraction, qd-algorithm"
}
@article{grag:74,
author = "W. B. Gragg",
year = "1974",
title = "Matrix Interpretations and Applications of the Continued
Fraction Algorithm",
journal = "Rocky Mountain Journal of Mathematics",
volume = "4",
pages = "213--???",
kwds = "la, continued fraction"
}
@article{grst:76,
author = "W. B. Gragg and G. W. Stewart",
year = "1976",
title = "A Stable Variant of the Secant Method for
Solving Nonlinear Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "13",
pages = "880--903",
kwds = "nla, nlop, secant method, condition estimation"
}
@article{grlt:79,
author = "W. B. Gragg and R. J. Leveque and J. A. Trangenstein",
year = "1979",
title = "Numerically Stable Methods for Updating Regressions",
journal = "Journal of the American Statistical Association",
volume = "74",
pages = "161-168",
kwds = "stat, nla, qrd, regr, lsq, updating"
}
@article{grha:84,
author = "W. B. Gragg and W. J. Harrod",
year = "1984",
title = "The Numerically Stable Reconstruction of {J}acobi Matrices from
Spectral Data",
journal = "Numerische Mathematik",
volume = "44",
pages = "317--336",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, inverse eigenvalue problem,
tridiagonal matrix"
}
@article{grag:86,
author = "W. B. Gragg",
year = "1986",
title = "The {QR} Algorithm for Unitary {H}essenberg Matrices",
journal = "Journal of Computational and Applied Mathematics",
volume = "16",
pages = "1--8",
note = "Cited in \cite{govl:89}.",
kwds = "nla, QR algorithm, unitary matrix, Hessenberg matrix, eig"
}
@article{grre:90,
author = "W. B. Gragg and L. Reichel",
year = "1990",
title = "A Divide and Conquer Method for Unitary and
Orthogonal Matrices",
journal = "Numerische Mathematik",
volume = "57",
pages = "695--718",
kwds = "nla, eig, orthogonal matrix, prll"
}
@techreport{grwa:90,
author = "W. B. Gragg and T.-L. Wang",
year = "1990",
title = "Convergence of the Shifted {QR}~Algorithm for
Unitary {Hessenberg} Matrices",
institution = "Naval Post Graduate School",
type = "Report",
number = "NPS-53-90-007",
kwds = "nla, eig, qr algorithm, orthogonal matrix, Hessenberg matrix"
}
@techreport{grwa:90a,
author = "W. B. Gragg and T.-L. Wang",
year = "1990",
title = "Convergence of the Unitary {Hessenberg} {QR}~Algorithm",
institution = "Naval Post Graduate School",
type = "Report",
number = "NPS-53-90-008",
kwds = "nla, eig, qr algorithm, orthogonal matrix, Hessenberg matrix"
}
@article{gram:1883,
author = "J. P. Gram",
year = "1883",
title = "{\"U}ber die {E}ntwicklung reeler {F}unctionen in
{R}eihen mittelst der {M}ethode der kleinsten {Q}uadrate",
journal = "{Journal f\"ur die reine und angewandte Mathematik}",
volume = "94",
pages = "41-73",
kwds = "math, Gram-Schmidt algorithm, orthogonalization"
}
@article{grth:85,
author = "W. K. Grassmann and M. I. Taksar and D. P. Heyman",
year = "1985",
title = "Regenerative Analysis and Steady State Distributions",
journal = "Operations Research",
volume = "33",
pages = "1107--1116",
kwds = "nla, Markov chain, lud"
}
@article{grau:71,
author = "A. A. Grau",
year = "1971",
title = "The Simultaneous {Newton} Improvement of a Complete Set
of Approximate Factors of a Polynomial",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "425--438",
kwds = "nlop, polynomial, Newton's method"
}
@book{gray:69,
author = "F. A. Graybill",
year = "1969",
title = "Introduction to Matrices with Applications in Statistics",
publisher = "Wadsworth",
address = "Belmont, California",
kwds = "book, stat, la, nla"
}
@article{gree:52,
author = "B. F. Green",
year = "1952",
title = "The Orthogonal Approximation of the Oblique Structure
in Factor Analysis",
journal = "Psychometrika",
volume = "17",
pages = "429--440",
kwds = "la, matrix approximation, Procrustes problem"
}
@phdthesis{gree:81,
author = "A. Greenbaum",
year = "1981",
title = "Convergence Properties of the Conjugate Gradient Algorithm
in Exact and Finite Precision Arithmetic",
school = "Department of Mathematics, University of California,
Berkeley",
kwds = "nla, conjugate gradients, rounding error"
}
@techreport{gree:81a,
author = "A. Greenbaum",
year = "1981",
title = "Behavior of the Conjugate Gradient Algorithm in Finite Precision
Arithmetic",
number = "UCRL 85752",
institution = "Lawrence Livermore Laboratory",
address = "Livermore, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, conjugate gradients"
}
@article{gree:89,
author = "A. Greenbaum",
year = "1989",
title = "Behavior of Slightly Perturbed Lanczos Conjugate Gradient
Recurrences",
journal = "Linear Algebra and Its Applications",
volume = "113",
pages = "7--63",
kwds = "nla, conjugate gradients, Lanczos algorithm, rounding error"
}
@article{gree:55,
author = "J. Greenstadt",
year = "1955",
title = "A Method for Finding Roots of Arbitrary Matrices",
journal = "Mathematical Tables and Other Aids to Computation",
volume = "9",
pages = "47--52",
kwds = "nla, eig, Jacobi-like, nonsymmetric matrix"
}
@article{gree:62,
author = "J. Greenstadt",
year = "1962",
title = "Some Numerical Experiments in Triangularizing Matrices",
journal = "Numerische Mathematik",
volume = "4",
pages = "187--195",
kwds = "nla, Jacobi-like, eig, nonsymmetric matrix"
}
@book{greu:67,
author = "W. H. Greub",
year = "1967",
title = "Linear Algebra",
publisher = "Springer-Verlag",
address = "New York",
kwds = "book, la"
}
@article{grev:74,
author = "T. N. E. Greville",
year = "1974",
title = "Solutions of the Matrix Equation {$XAX = X$} and Relations
between Oblique and Orthogonal Projectors",
journal = "SIAM Journal on Applied Mathematics",
volume = "26",
pages = "828--832",
kwds = "la, projection, ginv"
}
@phdthesis{grie:66,
author = "D. Gries",
year = "1966",
title = " {\"Uber einige Klassen von Normen}",
school = " {Technische Hochschule M\"unchen}",
kwds = "la, norm"
}
@article{grie:67,
author = "D. Gries",
year = "1967",
title = "Characterizations of Certain Classes of Norms",
journal = "Numerische Mathematik",
volume = "10",
pages = "30--41",
kwds = "la, norm"
}
@article{grst:67,
author = "D. Gries and J. Stoer",
year = "1967",
title = "Some Results on Fields of Values of Matrices",
journal = "SIAM Journal on Numerical Analysis",
volume = "4",
pages = "283--300",
kwds = "la, norm, field of values"
}
@article{gril:74,
author = "Z. Griliches",
year = "1974",
title = "Errors in Variables and Other Unobservables",
journal = "Econometrica",
volume = "42",
pages = "971-998",
kwds = "stat, eriv"
}
@article{grle:81,
author = "R. G. Grimes and J. G. Lewis",
year = "1981",
title = "Condition Number Estimation for Sparse Matrices",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "384--388",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, condition estimation"
}
@inproceedings{grgs:91,
author = "D. Gross and B. Gu and R. M. Soland",
year = "1991",
title = "The Biconjugate Gradient Method for Obtaining
the Steady-State Probability Distribution of
of Markovian Multiechelon Repairable Item
Inventory Systems",
booktitle = "Numerical Solution of {Markov} Chains",
editor = "W. J. Stewart",
pages = "473--489",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, conjugate gradients"
}
-gs- -gt- -gu-
@article{guco:88,
author = "L. Guangye and T. F. Colemnan",
year = "1988",
title = "A Parallel Triangular Solver for a Distributed
Memory Multiprocessor",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "485-502",
kwds = "prll, nla, message passing, triangular matrix"
}
@article{guwe:92,
author = "M. Gulliksson and P.-{\AA}. Wedin",
year = "1992",
title = "Modifying the {QR} Decomposition to Constrained and Weighted
Linear Least Squares",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "??",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, qrd, weights"
}
@article{guwm:76,
author = "R. F. Gunst and J. T. Webster and R. L. Mason",
year = "1976",
title = "A Comparison of Least Squares and
Latent Root Regression Estimators",
journal = "Technometrics",
volume = "18",
pages = "75--83",
note = "Cited in \cite{govl:89}.",
kwds = "stat, lsq, regr, svd, principal components, latent root regression"
}
@unpublished{guns:78,
author = "R. F. Gunst",
year = "1978?",
title = "Similarities among Least Squares, Principal Component,
and Latent Root Regression Estimators",
note = "Manuscript. Department of Statistics, Southern Methodist
University",
kwds = "stat, lsq, regr, svd, principal components, latent root regression"
}
@article{gupk:72,
author = "K. K. Gupta",
year = "1972",
title = "Solution of Eigenvalue Problems by {Sturm} Sequence
Method",
journal = "International Journal for Numerical Methods in Engineering",
volume = "4",
pages = "379--404",
kwds = "nla, eig, sparse, symmetric matrix, Sturm sequence"
}
@article{gupk:74,
author = "K. K. Gupta",
year = "1974",
title = "Eigenproblem Solution by a Combined {Sturm} Sequence
and Inverse Iteration Technique",
journal = "Int. J. Numer. Meth. Eng.",
volume = "8",
pages = "877-911",
kwds = "nla, eig, sparse, symmetric matrix, Sturm sequence,
inverse iteration"
}
@article{gupt:71,
author = "N. N. Gupta",
year = "1971",
title = "An Iterative Method for Computation of Generalized Inverse
and Matrix Rank",
journal = "IEEE Transactions on Systems, Man, and Cybernetics",
volume = "",
pages = "89--90",
kwds = "nla, ginv, iter"
}
@article{gupt:72,
author = "N. N. Gupta",
year = "1972",
title = "An Optimum Iterative Method for the Computation of Matrix
Rank",
journal = "IEEE Transactions on Systems, Man, and Cybernetics",
volume = "",
pages = "437--438",
kwds = "nla, ginv, iter, rank determination"
}
@article{gulw:70,
author = "F. G. Gustavson and W. Liniger and R. Willoughby",
year = "1970",
title = "Symbolic Generation of an Optimal {Crout} Algorithm for
Sparse Systems of Linear Equations",
journal = "Journal of the ACM",
volume = "17",
pages = "87--109",
kwds = "nla, lud, sparse, pivoting"
}
@inproceedings{gust:72,
author = "F. G. Gustavson",
year = "1972",
title = "Some Basic Techniques for Solving Sparse Systems
of Linear Equations",
booktitle = "Sparse Matrices and Their Applications",
editor = "D. J. Rose and R. A. Willoughby",
pages = "41--52",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, sparse, linear system"
}
@article{gumb:88,
author = "J. L. Gustafson and G. R. Montry and R. E. Benner",
year = "1988",
title = "Development of Parallel Methods for a 1024-Processor
Hypercube",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "609-638",
annote = "The paper that won the Karp and Bell awards",
kwds = "na, prll, hypercube, communication, message passing, pde"
}
@article{gutk:72,
author = "M. H. Gutknecht",
year = "1972",
title = "{\it A Posteriori\/} Error Bounds for the Zeros of a Polynomial",
journal = "Numerische Mathematik",
volume = "20",
pages = "139--148",
kwds = "nlop, polynomial, pert"
}
@techreport{gutk:90,
author = "M. H. Gutknecht",
year = "1990",
title = "A Complete Theory of the Unsymmetric Lanczos Process
and Related Algorithms: Part {I}",
institution = "Interdisciplinary Project Center for Supercomputing,
Eidgen{\"o}ssische Technische Hochschule Z{\"u}ich",
type = "Research Report",
number = "90-10",
kwds = "nla, eig, Lanczos algorithm, nonsymmetric matrix"
}
@techreport{gutk:90a,
author = "M. H. Gutknecht",
year = "1990",
title = "A Complete Theory of the Unsymmetric Lanczos Process
and Related Algorithms: Part {II}",
institution = "Interdisciplinary Project Center for Supercomputing,
Eidgen{\"o}ssische Technische Hochschule Z{\"u}ich",
type = "Research Report",
number = "90-16",
kwds = "nla, eig, Lanczos algorithm, nonsymmetric matrix"
}
@techreport{gutk:91,
author = "M. H. Gutknecht",
year = "1991",
title = "On Certain Types of $(k,l)$-Step Methods for Solving
Linear Systems of Equations",
institution = "Interdisciplinary Project Center for Supercomputing,
Eidgen{\"o}ssische Technische Hochschule Z{\"u}ich",
type = "Research Report",
number = "91-01",
kwds = "nla, linear system, sparse, iter"
}
@techreport{gutk:91a,
author = "M. H. Gutknecht",
year = "1991",
title = "Changing the Norm in Conjugate Gradient Type Algorithms",
institution = "Interdisciplinary Project Center for Supercomputing,
Eidgen{\"o}ssische Technische Hochschule Z{\"u}ich",
type = "Research Report",
number = "91-15",
kwds = "nla, conjugate gradients, preconditioning,"
}
@techreport{gutk:91b,
author = "M. H. Gutknecht",
year = "1991",
title = "Variants of {\sc BiCGStab} for Matrices with Complex
Spectrum",
institution = "Interdisciplinary Project Center for Supercomputing,
Eidgen{\"o}ssische Technische Hochschule Z{\"u}ich",
type = "Research Report",
number = "91-14",
kwds = "nla, biconjugate gradients"
}
@article{gutk:92,
author = "M. H. Gutknecht",
year = "1992",
title = "A Complete Theory of the Unsymmetric Lanczos Process
and Related Algorithms: Part {I}",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "594--639",
kwds = "nla, eig, Lanczos algorithm, nonsymmetric matrix"
}
-gv- -gw- -gx- -gy- -gz-
-ha-
@book{habe:74,
author = "S. J. Haberman",
year = "1974",
title = "The Analysis of Frequency Data",
publisher = "The University of Chicago Press",
address = "Chicago",
kwds = "book, stat, categorical data, log-linear model"
}
@article{habe:74a,
author = "S. J. Haberman",
year = "1974",
title = "Log-Linear Models for Frequency Tables with Ordered
Classifications",
journal = "Biometrics",
volume = "30",
pages = "589--600",
kwds = "stat, log-linear model, categorical data"
}
@article{habe:75,
author = "S. J. Haberman",
year = "1975",
title = "How Much Do {Gauss--Markov} and Least Square Estimates Differ?
{A} Coordinate-Free Approach",
journal = "Annals of Statistics",
volume = "3",
pages = "982-990",
kwds = "stat, lsq, Gauss-Markov theorem"
}
@incollection{hach:74,
author = "G. D. Hachtel",
year = "1974",
title = "Extended Applications of the Sparse Tableau Approach---Finite
Elements and Least Squares",
booktitle = "Basic questions in design theory",
editor = "W. Spillers",
publisher = " North-Holland",
address = "Amsterdam",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{hada:1892,
author = "M. J. Hadamard",
year = "1892",
title = "Essai sur l'\'etude des fonctions donn\'ees par
leur d\'eveloppement de Taylor",
journal = "Journ.\ de Math. ($4^{\rm e}$ {\rm s\'erie})",
volume = "8",
pages = "101--186",
kwds = "nlop"
}
@article{hapo:75,
author = "L. A. Hageman and T. A. Porsching",
year = "1975",
title = "Aspects of Nonlinear Block Successive Overrelaxation",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "316--335",
kwds = "nla, linear system, relaxation"
}
@article{haly:80,
author = "L. A. Hageman and F. T. Luk and D. M. Young",
year = "1980",
title = "On the Equivalence of Certain Iterative Acceleration Methods",
journal = "SIAM Journal on Numerical Analysis",
volume = "17",
pages = "852--873",
kwds = "nla, linear system, iter, sparse"
}
@book{hayo:81,
author = "L. A. Hageman and D. M. Young",
year = "1981",
title = "Applied Iterative Methods",
publisher = "Academic Press",
address = "New York and London",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, iter"
}
@article{hage:84,
author = "W. W. Hager",
year = "1984",
title = "Condition Estimators",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "5",
pages = "311--316",
note = "Cited in \cite{high:87}.",
kwds = "nla, condition estimation"
}
@article{hahn:27,
author = "H. Hahn",
year = "1927",
title = " {\"Uber lineare Gleichungs\-systeme in linearen R\"aumen}",
journal = "{Journal f\"ur die reine und angewandte Mathematik}",
volume = "157",
pages = "214-229",
kwds = "la, Hahn-Banach theorem, functional analysis"
}
@book{hald:75,
author = "A. Hald",
year = "1974",
title = "Statistical Theory and Engineering Applications",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, stat, Hald data, regr"
}
@article{hall:35,
author = "P. Hall",
year = "1935",
title = "On Representation of Subsets",
journal = "Journal of the London Mathematical Society",
volume = "10",
pages = "26--30",
kwds = "math, Koenig-Frobenius theorem"
}
@article{halm:50,
author = "P. R. Halmos",
year = "1950",
title = "Normal Dilations and Extensions of Operators",
journal = "Summa Brasiliensis Math.",
volume = "2",
pages = "125-134",
note = "Cited in \cite{szna:60}.",
kwds = "la, dilation, functional analysis"
}
@book{halm:58,
author = "P. R. Halmos",
year = "1958",
title = "Finite-Dimensional Vector Spaces",
publisher = "Van Nostrand",
address = "Princeton, New Jersey",
note = "2nd Edition",
kwds = "book, la"
}
@article{hamm:74,
author = "S. Hammarling",
year = "1974",
title = "A Note on Modifications to the {Givens} Plane Rotations",
journal = "J.\ Inst.\ Math.\ Appl.",
volume = "13",
pages = "215--218",
note = "Cited in \cite{govl:89}",
kwds = "nla, plane rotation, fast algorithm"
}
@article{hamm:85,
author = "S. J. Hammarling",
year = "1985",
title = "The Singular Value Decomposition in Multivariate Statistics",
journal = "{ACM} {SIGNUM} Newsletter",
volume = "20",
pages = "2--25",
note = "Cited in \cite{govl:89}.",
kwds = "nla, stat, svd, multivariate analysis"
}
@article{hans:62,
author = "E. R. Hansen",
year = "1962",
title = "On Quasicyclic {J}acobi Methods",
journal = "Journal of the {ACM}",
volume = "9",
pages = "118--135",
note = "Cited in \cite{govl:89}.",
kwds = "nla"
}
@article{hans:63,
author = "E. R. Hanson",
year = "1963",
title = "On Cyclic {J}acobi Methods",
journal = "{SIAM} Journal on Applied Mathematics",
volume = "11",
pages = "448--459",
note = "Cited in \cite{govl:89}.",
kwds = "nla"
}
@article{hans:87,
author = "P. C. Hansen",
year = "1987",
title = "The Truncated SVD as a Method for Regularization",
journal = "BIT",
volume = "27",
pages = "534--553",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, regularization"
}
@article{hans:87a,
author = "P. C. Hansen",
year = "1987",
title = "Detection of Near-Singularity in Cholesky and
${LDL^T}$ Factorizations",
journal = "J. Comput. Appl. Math.",
volume = "19",
pages = "293--299",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, Cholesky decomposition, rank determination"
}
@incollection{hans:88,
author = "P. C. Hansen",
year = "1988",
title = "Reducing the Number of Sweeps in {H}estenes Method",
booktitle = "Singular Value Decomposition and Signal Processing",
editor = "E. F. Deprettere",
publisher = "North-Holland",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, Hestenes method"
}
@article{hans:88a,
author = "P. C. Hansen",
year = "1988",
title = "The 2-Norm of Random Matrices",
journal = "J. Comput. Appl. Math.",
volume = "23",
pages = "117--120",
note = "Citation communicated by Per Christian Hansen.",
kwds = "la, norm, random matrix"
}
@techreport{hans:89,
author = "P. C. Hansen",
year = "1989",
title = "Relations between {SVD} and {GSVD} of Discrete
Regularization Problems in Standard and General Form",
institution = "Computational and Applied Mathematics, Department
of Mathematics, University of California at
Los Angeles",
type = "CAM Report",
number = "89--03",
kwds = "nla, svd, gsvd, regularization"
}
@techreport{hans:89b,
author = "P. C. Hansen",
year = "1989",
title = "Regularization, {GSVD} and Truncated {GSVD}",
institution = "Computational and Applied Mathematics, Department
of Mathematics, University of California at
Los Angeles",
type = "CAM Report",
number = "89--10",
kwds = "nla, gsvd, regularization"
}
@article{hans:90,
author = "P. C. Hansen",
year = "1990",
title = "Truncated Singular Value Decomposition Solutions to Discrete
Ill-Posed Problems with Ill-Determined Numerical Rank",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "11",
pages = "503--518",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, ill-posed problem, rank determination, regularization"
}
@techreport{hass:91,
author = "P. C. Hansen and T. Sekii and H. Shibahashi",
year = "1991",
title = "The Modified Truncated-SVD Method for Regularization
in General form",
institution = "Department of Astronomy, University of Tokyo",
note = "To appear in {\it SIAM Journal on Scientific and
Statistical Computing.\/}",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, regularization, qrd"
}
@article{hala:69,
author = "R. J. Hanson and R. J. Lawson",
year = "1969",
title = "Extensions and Applications of the Householder Algorithm for
Solving Linear Least Squares Problems",
journal = "Mathematics of Computation",
volume = "23",
pages = "787--812",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, lsq, Householder transformation"
}
@article{haph:75,
author = "R. J. Hanson and J. L. Phillips",
year = "1975",
title = "An Adaptive Numerical Method for Solving Linear Fredholm
Equations of the First Kind",
journal = "Numer. Math.",
volume = "24",
pages = "291--307",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "na, integral equation, regularization"
}
@article{hano:81,
author = "R. J. Hanson and M. J. Norris",
year = "1981",
title = "Analysis of Measurements Based on the Singular Value
Decomposition",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "2",
pages = "363--374",
note = "Cited in \cite{govl:89}.",
kwds = "stat, nla, svd"
}
@article{hans:86,
author = "R. J. Hanson",
year = "1986",
title = "Linear Least Squares with Bounds and Linear Constraints",
journal = " SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "826--834",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints"
}
@article{hari:82,
author = "V. Hari",
year = "1982",
title = "On the Global Convergence of the {E}berlein Method
for Real Matrices",
journal = "Numerische Mathematik",
volume = "39",
pages = "361--370",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Eberlein's method, Jacobi-like"
}
@phdthesis{hari:84,
author = "V. Hari",
year = "1984",
title = "On Cyclic {Jacobi} Methods for the Positive Definite Generalized
Eigenvalue Problem",
school = "Fachbereich Mathematik und Informatik der
Fernuniversit{\"a}t---Gesamthochschule---Hagen",
kwds = "nla, geig, Jacobi-like, symmetric matrix"
}
@article{hakr:87,
author = "V. Hari and K. Veseli\`c",
year = "1987",
title = "On {Jacobi} Methods for Singular Value Decompositions",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "741-754",
kwds = "nla, svd, Jacobi-like"
}
@techreport{hari:90,
author = "V. Hari",
year = "1990",
title = "On Sharp Quadratic Convergence Bounds for the
Serial Jacobi Methods",
institution = "Army High Performance Computing Research Center,
Univeristy of Minnesota",
type = "Prepring",
number = "90-38",
kwds = "nla, Jacobi's method"
}
@article{hapl:84,
author = "W. Harrod and R. J. Plemmons",
year = "1984",
title = "Comparison of Some Direct Methods for Computing
Stationary Distributions of {Markov} Chains",
journal = "SIAM Journal of Scientific and Statistical Computing",
volume = "5",
pages = "453--469",
kwds = "nla, Markov chain, test matrix"
}
@article{haha:81,
author = "K. H. Haskell and R. J. Hanson",
year = "1981",
title = "An Algorithm for Linear Least Squares Problems with Equality
and Nonnegativity Constraints",
journal = "Mathematical Programming",
volume = "21",
pages = "98--118",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints"
}
@unpublished{haha:91,
author = "R. Hassin and M. Haviv",
year = "1991",
title = "Mean Passage Times and Nearly Uncoupled Markov
Chains",
note = "Manuscript, Department of Statistsics, Hebrew
University of Jerusalem.",
kwds = "la, Markov chain, nearly uncoupled system"
}
@book{haus:14,
author = "F. Hausdorff",
year = "1914",
title = " {Grundz\"uge der Mengenlehre}",
publisher = "Chelsea",
address = "New York",
note = "Reprinted by Chelsea, 1949.",
kwds = "book, math, Hausdorff metric"
}
@article{haus:19,
author = "F. Hausdorff",
year = "1919",
title = "{Das Wertvorrat einer Bilinearform}",
journal = "Mathematische Zeitschrift",
volume = "3",
pages = "314-316",
kwds = "la, field of values"
}
@article{hahe:84,
author = "M. Haviv and van der Heyden, L.",
year = "1984",
title = "Perturbation Bounds for the Stationary Probabilities of
a Finite {Markov} Chain",
journal = "Advances in Applied Probability",
volume = "16",
pages = "804-818",
kwds = "la, pert, Markov chain, eig"
}
@unpublished{havi:8?,
author = "M. Haviv",
year = "198?",
title = "The Stationary Distribution of a Nearly Completely
Decomposabel {Markov} Chain",
note = "Manuscript. Department of Statistics, The Hebrew University",
kwds = "nla, Markov chain, eig, sparse"
}
@article{havi:87,
author = "M. Haviv",
year = "1987",
title = "Aggregration/Disaggregation Methods for Computing
the Stationary Distribution of a {Markov} Chain",
journal = "SIAM Journal on Numerical Analysis",
volume = "24",
pages = "952-966",
kwds = "nla, Markov chain, eig, aggregation"
}
@unpublished{hari:89,
author = "M. Haviv and Y. Ritov",
year = "1989",
title = "Series Expansions for Stochastic Matrices",
note = "Manuscript, Department of Statistsics, Hebrew
University of Jerusalem. This note appeared in
in the pre-conference proceedings of the Internationl
Workshop on the Numerical Solution of Markov Chains,
Raleigh, NC.",
kwds = "la, Markov chain, nearly uncoupled system"
}
@unpublished{havi:91,
author = "M. Haviv",
year = "1991",
title = "A New Rank-One Replacement Algorithm for Computing
The Stationary Distribution of a Large Markov
Chain",
note = "Manuscript, Department of Statistsics, Hebrew
University of Jerusalem.",
kwds = "nla, Markov chain, nearly uncoupled system"
}
@article{hawk:73,
author = "D. M. Hawkins",
year = "1973",
title = "On the Investigation of Alternative Regressions by
Principal Component Analysis",
journal = "Appl.\ Statist.",
volume = "22",
pages = "275--286",
kwds = "stat, regr, svd, principal components"
}
@article{hawk:77,
author = "Thomas Hawkins",
year = "1977",
title = "Weierstrass and the Theory of Matrices",
journal = "Archive for History of Exact Sciences",
volume = "17",
pages = "119-163",
kwds = "la, history, matrix theory, Weierstrass"
}
-hb- -hc- -hd- -he-
@article{heev:68,
author = "J. Z. Hearon and J. W. Evans",
year = "1968",
title = "Differentiable Generalized Inverses",
journal = "Journal of Research of the National Bureau
of Standards, Series B",
volume = "72",
pages = "109--113",
kwds = "la, pert, ginv, matrix derivative"
}
@phdthesis{heat:78,
author = "M. T. Heath",
year = "1978",
title = "Numerical Algorithms for Nonlinearly Constrained Optimization",
number = "STAN-CS-78-656",
school = "Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nlop, constraints"
}
@unpublished{heat:82,
author = "M. T. Heath",
year = "1982",
title = "Sparse Matrix Software Catalog. {Sparse} Matrix Symposium 1982",
note = "Bound report. Mathematics and Statistics Research Department,
Oak Ridge National Laboratory",
kwds = "nla, sparse, software"
}
@article{heat:82a,
author = "M. T. Heath",
year = "1982",
title = "Some extensions of an algorithm for sparse linear least
squares problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "3",
pages = "223--237",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, lsq, sparse, rank determination"
}
@article{heat:84,
author = "M. T. Heath",
year = "1984",
title = "Numerical Methods for Large Sparse Linear Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing,",
volume = "5",
pages = "497--513",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@techreport{heat:85,
author = "M. T. Heath",
year = "1985",
title = "Parallel {Cholesky} Factorization in Message-Passing
Multiprocessor Environments",
institution = "Mathematical Sciences Section, Oak Ridge
National Laboratory",
number = "ORNL-6150",
kwds = "nla, prll, Cholesky decomposition, message passing"
}
@proceedings{heat:86,
editor = "M. T. Heath",
year = "1986",
title = "Proceedings of First {SIAM} Conference on Hypercube
Multiprocessors",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll, hypercube"
}
@article{heso:86,
author = "M. T. Heath and D. C. Sorensen",
year = "1986",
title = "A Pipelined Method for Computing the {QR} Factorization of a Sparse
Matrix",
journal = "Linear Algebra and its Applications",
volume = "77",
pages = "189--203",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vect, qrd, sparse"
}
@proceedings{heat:87,
editor = "M. T. Heath",
year = "1987",
title = "Hypercube Multiprocessors",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll, hypercube"
}
@article{help:86,
author = "M. T. Heath and A. J. Laub and C. C. Paige and R. C. Ward",
year = "1986",
title = "Computing the {SVD} of a Product of Two Matrices",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "1147--1149",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, gsvd, svd"
}
@article{hero:88,
author = "M. T. Heath and C. H. Romine",
year = "1988",
title = "Parallel Solution of Triangular Systems on
Distributed Memory Multiprocessors",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "558-588",
kwds = "nla, prll, triangular matrix, message passing"
}
@article{hejb:85,
author = "M. T. Heideman and D. H. Johnson and C. S. Burrus",
year = "1985",
title = "Gauss and the History of the {Fast Fourier Transform}",
journal = "Archive for History of Exact Sciences",
volume = "34",
pages = "265-267",
kwds = "history, fft, fast algorithm, Gauss"
}
@article{heig:78,
author = "R. M. Heigberger",
year = "1978",
title = "Generation of Random Orthogonal Matrices",
journal = "Applied Statistics",
volume = "27",
pages = "199-206",
kwds = "stat, nla, random matrix, orthogonal matrix"
}
@article{hewa:89,
author = "C. E. Heil and D. F. Walnut",
year = "1989",
title = "Continuous and Discrete Wavelet Transforms",
journal = "SIAM Review",
volume = "31",
pages = "628--666",
kwds = "math, wavelet"
}
@article{hell:76,
author = "D. Heller",
year = "1976",
title = "Some Aspects of the Cyclic Reduction Algorithm for Block
Tridiagonal Linear Systems",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "13",
pages = "484--496",
note = "Cited in \cite{govl:89}.",
kwds = "nla, cyclic reduction, block algorithm, block tridiagonal matrix"
}
@article{hell:78,
author = "D. Heller",
year = "1978",
title = "A Survey of Parallel Algorithms in Numerical Linear Algebra",
journal = "{SIAM} Review",
volume = "20",
pages = "740--777",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll"
}
@article{heip:83,
author = "D. E. Heller and I. C. F. Ipsen",
year = "1983",
title = "Systolic Networks for Orthogonal Decompositions",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "4",
pages = "261--269",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, systolic"
}
@book{helm:80,
author = "F. R. Helmert",
year = "1880",
title = "{Die Mathematischen und Physikalischen Theorien der h{\"o}heren
Geod{\"a}sie, 1 Teil}",
publisher = "Teubner",
address = "Leipzig",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, lsq, geodesy, nested dissection"
}
@article{helt:68,
author = "B. W. Helton",
year = "1968",
title = "Logarithms of Matrices",
journal = "Proceedings of the American Mathematical Society",
volume = "19",
pages = "733--736",
note = "Cited in \cite{govl:89}.",
kwds = "math, matrix function, matrix logarithm"
}
@article{hemm:79,
author = "W. J. Hemmerle",
year = "1979",
title = "Balanced Hypotheses and Unbalanced Data",
journal = "Journal of the American Statistical Association",
volume = "74",
pages = "794-798",
kwds = "stat, anova, hypothesis testing"
}
@article{hese:81,
author = "H. V. Henderson and S. R. Searle",
year = "1981",
title = "On Deriving the Inverse of a Sum of Matrices",
journal = "SIAM Review",
volume = "23",
pages = "53-60",
kwds = "la, inverse matrix"
}
@inproceedings{hehp:88,
author = "C. S. Henkel and M. T. Heath and R. J. Plemmons",
year = "1988",
title = "{C}holesky Downdating on a Hypercube",
booktitle = "The Third Conference on Hypercube Concurrent Computers and
Applications, Vol. {II}, Applications",
editor = "G. Fox",
publisher = "{ACM} Press",
address = "New York",
pages = "1592--1598",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Cholesky decomposition, updating, prll, hypercube"
}
@article{hepl:91,
author = "C. S. Henkel and R. J. Plemmons",
year = "1991",
title = "Recursive Least Squares on a Hypercube Multiprocessor
Using the Covariance Factorization",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "95--106",
kwds = "nla, lsq, updating, prll, hypercube"
}
@article{henr:58,
author = "P. Henrici",
year = "1958",
title = "On the Speed of Convergence of Cyclic and Quasicyclic
{Jacobi} Methods for Computing Eigenvalues of {Hermitian}
Matrices",
journal = "Joural of the Society for Industrial and Applied
Mathematics",
volume = "6",
pages = "144--162",
kwds = "nla, eig, Jacobi's method, symmetric matrix"
}
@article{henr:62,
author = "P. Henrici",
year = "1962",
title = "Bounds for Iterates, Inverses, Spectral Variation
and Fields of Values of Nonnormal Matrices",
journal = "Numerische Mathematik",
volume = "4",
pages = "24--39",
kwds = "la, pert, eig, inverse matrix, field of values,
nonnormal matrix"
}
@article{henr:65,
author = "P. Henrici",
year = "1965",
title = "Finding Zeros of a Polynomial by the Q-D Algorithm",
journal = "Communications of the ACM",
volume = "8",
pages = "570--574",
kwds = "nlop, polynomial, qd-algorithm"
}
@article{hezi:68,
author = "P. Henrici and K. Zimmermann",
year = "1968",
title = "An Estimate for the Norms of Certain cyclic {J}acobi Operators",
journal = "Linear Algebra and its Applications",
volume = "1",
pages = "489--501",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method"
}
@article{henr:70,
author = "P. Henrici",
year = "1970",
title = "Methods of Search for Solving Polynomial Equations",
journal = "Journal of the ACM",
volume = "17",
pages = "273--283",
kwds = "nlop, polynomial, Lehmer's method"
}
@book{henr:74,
author = "P. Henrici",
year = "1974",
title = "Applied and Complex Analysis. V1",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, math"
}
@article{herm:1857,
author = "C. Hermite",
year = "1857",
title = " {Extrait d'une lettre de M. C. Hermite \`a
M. Borchardt sur l'invariabilit\'e des carr\'es
positifs et des carr\'es n\'egatifs dans la transformation
des polynomes homog\`enes du second degr\'e}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "53",
pages = "271--274",
kwds = "la, inertia, history, Jacobi, Hermite"
}
@article{herr:80,
author = "D. G. Herr",
year = "1980",
title = "On the History of the Use of Geometry in the General Linear Model",
journal = "The American Statistician",
volume = "b 34",
pages = "43-47",
kwds = "stat, regr, history"
}
@article{heka:51,
author = "M. R. Hestenes and W. Karush",
year = "1951",
title = "A Method of Gradients for the Calculation of the
Characteristic Roots and Vectors of a Real Symmetric
Matrix",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "47",
pages = "45--61",
kwds = "nla, eig, symmetric matrix, sparse"
}
@article{heka:51a,
author = "M. R. Hestenes and W. Karush",
year = "1951",
title = "Solutions of {$Ax = \lambda Bx$}",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "47",
pages = "471--478",
kwds = "nla, geig, sparse, symmetric matrix"
}
@techreport{hest:51b,
author = "M. R. Hestenes",
year = "1951",
title = "Iterative Methods for Solving Linear Equations",
institution = "NAML",
type = "Report",
number = "52-9",
note = "Reprinted in Journal of Opeimization Theory and
Applications, Volume 11, pp. 323--334, 1973",
kwds = "nla, conjugate gradients"
}
@article{hest:52,
author = "M. R. Hestenes and E. Stiefel",
year = "1952",
title = "Methods of Conjugate Gradients for Solving Linear
Systems",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "49",
pages = "409--436",
kwds = "nla, linear system, conjugate gradients"
}
@article{hest:58,
author = "M. R. Hestenes",
year = "1958",
title = "Inversion of Matrices by Biorthogonalization and Related Results",
journal = "SIAM Journal",
volume = "6",
pages = "51--90",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, conjugate gradients, inverse matrix, Lanczos algorithm"
}
@article{hest:68,
author = "M. R. Hestenes",
year = "1968",
title = "Pairs of Quadratic Forms",
journal = "Linear Algebra and Its Applications",
volume = "1",
pages = "397--407",
kwds = "la, geig, matrix pencil, symmetric matrix"
}
@article{hest:75,
author = "M. R. Hestenes",
year = "1975",
title = "Pseudoinverses and Conjugate Gradients",
journal = "Communications of the ACM",
volume = "18",
pages = "40--43",
kwds = "nla, ginv, conjugate gradients"
}
@book{hest:80,
author = "M. R. Hestenes",
year = "1980",
title = "Conjugate Direction Methods in Optimization",
publisher = "Springer-Verlag",
address = "Berlin",
note = "Cited in \cite{govl:89}.",
kwds = "book, nlop, conjugate direction, conjugate gradients"
}
@inproceedings{herz:49,
author = "M. Herzberger",
year = "1949",
title = "The Normal Equations of the Method of Least Squares and Their
Solution",
booktitle = "Quarterly of Applied Mathematics.",
kwds = "math, lsq, normal equations"
}
@book{hese:77,
author = "C. C. Heyde and E. Senta",
year = "1977",
title = "I.J. Bienaym\'e, Stastical Theory Anticipated",
publisher = "Springer",
address = "New York",
kwds = "book, stat, history, Bienayme"
}
-hf- -hg- -hh- -hi-
@article{hieb:86,
author = "K. L. Hiebert",
year = "1986",
title = "An Evaluation of Mathematical Software that Solves Nonlinear
Least Squares Problems",
journal = "ACM Transactions on Mathematical Software",
volume = "7",
pages = "1--16",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@phdthesis{high:85,
author = "N. J. Higham",
year = "1985",
title = "Nearness Problems in Numerical Linear Algebra",
school = "University of Manchester",
address = "England",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pert"
}
@article{high:86,
author = "N. J. Higham",
year = "1986",
title = "Computing the Polar Decomposition--with Applications",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "1160--1174",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, polar decomposition"
}
@article{high:86a,
author = "N. J. Higham",
year = "1986",
title = "{N}ewton's Method for the Matrix Square Root",
journal = "Mathematics of Computation",
volume = "46",
pages = "537--550",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix square root, Newton's method"
}
@article{high:86b,
author = "N. J. Higham",
year = "1986",
title = "Efficient Algorithms for computing the condition number of a
tridiagonal matrix",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "7",
pages = "150--165",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition estimation, tridiagonal matrix"
}
@inproceedings{hist:87,
author = "N. J. Higham and G. W. Stewart",
year = "1987",
title = "Numerical Linear Algebra in Statistical Computing",
booktitle = "The State of the Art in Numerical Analysis",
editor = "A. Iserles and M. J. D. Powell",
pages = "41--57",
publisher = "Clarendon Press",
address = "Oxford",
kwds = "nla, stat"
}
@article{high:87,
author = "N. J. Higham",
year = "1987",
title = "A Survey of Condition Number Estimation for Triangular
Matrices",
journal = "SIAM Review",
volume = "29",
pages = "575-596",
kwds = "nla, condition estimation, triangular matrix"
}
@article{high:87a,
author = "N. J. Higham",
year = "1987",
title = "Error Analysis of the {B}j{\"o}rck-{P}ereyra Algorithms for Solving
{V}andermonde Systems",
journal = "Numerische Mathematik",
volume = "50",
pages = "613--632",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, Vandermonde matrix, rounding error"
}
@article{high:87b,
author = "N. J. Higham",
year = "1987",
title = "Computing Real Square Roots of a Real Matrix",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "405--430",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix square root"
}
@article{high:88,
author = "N. J. Higham",
year = "1988",
title = "Computing a Nearest Symmetric Positive Semidefinite
Matrix",
journal = "Linear Algebra and Its Applications",
volume = "103",
pages = "103-118",
kwds = "nla, matrix approximation"
}
@article{high:88a,
author = "N. J. Higham",
year = "1988",
title = "FORTRAN Codes for Estimating the One-norm of a Real or Complex
Matrix, with Applications to Condition Estimation",
journal = "ACM Transactions on Mathematical Software",
volume = "14",
pages = "381--396",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition estimation, software"
}
@article{high:88b,
author = "N. J. Higham",
year = "1988",
title = "The Symmetric {P}rocrustes Problem",
journal = "{BIT}",
volume = "28",
pages = "133--143",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Procrustes problem, symmetric matrix"
}
@article{high:88c,
author = "N. J. Higham",
year = "1988",
title = "Fast Solution of {V}andermonde-like Systems Involving Orthogonal
Polynomials",
journal = "{IMA} Journal of Numerical Analysis",
volume = "8",
pages = "473--486",
note = "Cited in \cite{govl:89}.",
kwds = "nla, fast algorithm, linear system, Vandermonde matrix,
orthogonal polynomial"
}
@techreport{high:88d,
author = "N. J. Higham",
year = "1988",
title = "The Accuracy of Solutions to Triangular Systems",
Number = 158,
institution = "Mathematics, University of Manchester",
address = "England",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, triangular matrix, linear system"
}
@techreport{hisc:88,
author = "N. J. Higham and R. S. Schreiber",
year = "1988",
title = "Fast Polar Decomposition of an Arbitrary Matrix",
number = "88-942",
institution = "Computer Science, Cornell University",
address = "Ithaca, NY 14853",
note = "Cited in \cite{govl:89}.",
kwds = "nla, polar decomposition, fast algorithm"
}
@incollection{high:89,
author = "N. J. Higham",
year = "1989",
title = "Analysis of the {C}holesky Decomposition of a
Semi-definite Matrix",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. J. Hammarling",
publisher = "Oxford University Press",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Cholesky decomposition, semi-definite matrix, rounding error"
}
@techreport{high:89a,
author = "N. J. Higham",
year = "1989",
title = "How Accurate is {Gaussian} Elimination?",
institution = "Department of Computer Science, Cornell University",
type = "Technical Report",
number = "TR 89-1024",
note = "To appear in the proceedings of the 13th Dundee Biennial Conference
on Numerical Analysis.",
kwds = "nla, lud, rounding error"
}
@techreport{high:89b,
author = "N. J. Higham",
year = "1989",
title = "Exploiting Fast Matrix Multiplication within the Level~3 {BLAS}",
institution = "Department of Computer Science, Cornell University",
type = "Technical Report",
number = "89-984",
note = "To appear in {\it ACM Tran. Math. Soft.\/}",
kwds = "nla, matrix multiplication, fast algorithm"
}
@article{hihi:89,
author = "N. J. Higham and D. J. Higham",
year = "1989",
title = "Large Growth Factors in {G}aussian Elimination with Pivoting",
journal = "{SIAM} Journal on Matrix Analysis and Applications",
volume = "10",
pages = "155--164",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, lud, pivoting"
}
@inproceedings{high:90,
author = "N. J. Higham",
year = "1990",
title = "Computing Error Bounds for Regression Problems",
booktitle = "Contemporary Mathematics 112: Statistical
Analysis of Measurement Error Models and
Applications",
editor = "P. J. Brown and W. A. Fuller",
pages = "195--210",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
kwds = "stat, nla, pert, regr, lsq, backward perturbation"
}
@techreport{high90a,
author = "N. J. Higham",
year = "1990",
title = "Stability of a Method for Multiplying Complex
Matrices with Three Real Matrix Multiplications",
institution = "University of Manchester",
type = "Numerical Analysis Report",
number = "181",
kwds = "nla, matrix multiplication, rounding error"
}
@techreport{high:90b,
author = "N. J. Higham",
year = "1990",
title = "Iterative Refinement Enhances the Stability of
{$QR$}~Factorization Methods for Solving Linear
Equations",
institution = "Department of Mathematics, University of Manchester",
type = "Numerical Analysis Report",
number = "182",
kwds = "nla, rounding error, iterative refinement, qrd"
}
@inproceedings{high:90c,
author = "N.J. Higham",
year = 1990,
title = "How Accurate is {Gaussian} Elimination?",
booktitle = "Numerical Analysis 1989, Proceedings of the 13th
Dundee Conference",
editor = "D.F. Griffiths and G.A. Watson",
pages = "137-154",
publisher = "Longman Scientific and Technical",
kwds = "nla, lud, rounding error"
}
@inproceedings{high:90d,
author = "N.J. Higham",
year = 1990,
title = "Analysis of the {Cholesky} Decomposition of a
Semi-definite Matrix",
booktitle = "Reliable Numerical Computation",
editor = "M.G. Cox and S.J. Hammarling",
pages = "161-185",
publisher = "Clarenden Press",
address = "Oxford",
kwds = "nla, lud, Cholesky decomposition, rounding error"
}
@article{high:90e,
author = "N. J. Higham",
year = "1990",
title = "Experience with a Matrix Norm Estimator",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "11",
pages = "804--809",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition estimation"
}
@unpublished{hihi:91,
author = "D. J. Higham and N. J. Higham",
year = "1991",
title = "Componentwise Perturbation Theory for Linear
Systems with Multiple Right-Hand Sides",
note = "Department of Mathematics, University of
Manchester",
kwds = "la, pert, structured perturbation,
backward perturbation, linear system"
}
@techreport{high:91,
author = "N. J. Higham",
year = "1991",
title = "Estimating the Matrix $p$-norm",
institution = "Department of Mathematics, University of Manchester",
type = "Numerical Analysis Report",
number = "202",
kwds = "nla, condition estimation, Hoelder norm"
}
@article{high:91a,
author = "N. J. Higham",
year = "1991",
title = "Iterative Refinement Enhances the Stability of {QR} Factorization
Methods for Solving Linear Equations",
journal = "BIT",
volume = "31",
pages = "447-468",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, qrd, iterative refinement"
}
@techreport{hikn:91,
author = "N. J. Higham and P. A. Knight",
year = "1991",
title = "Component Error Analysis for Stationary Iterative
Methods",
institution = "Department of Mathematics, University of Manchester",
type = "Numerical Analysis Report",
number = "206",
kwds = "nla, linear system, iter, pert"
}
@techreport{hill:77,
author = "E. M. Hill",
year = "1977",
title = "Computer Solution of Large Dense Linear Problems",
institution = "Computer Science Center, University of Maryland",
type = "Technical Report",
number = "TR-576",
kwds = "nla, linear system, memory hierarchy"
}
@techreport{hipa:91,
author = "R. O. Hill and B. N. Parlett",
year = "1991",
title = "Refined Interlacing Properties",
institution = "Center for Pure and Applied Mathematics,
University of California, Berkeley",
type = "Report",
number = "PAM-517",
kwds = "nla, eig, symmetric matrix"
}
@article{hirs:02,
author = "A. Hirsch",
year = "1902",
title = "Sur les racines d'une equation fondementale
{Extrait d'une lettre de M. A. Hirsch {\`a} M. I. Bendixson}",
journal = "Acta Mathematica",
volume = "25",
pages = "367-370",
kwds = "la, eig, Bendixson's theorem"
}
-hj- -hk- -hl- -hm- -hn- -ho-
@article{hoag:72,
author = "D. C. Hoaglin",
year = "1972",
title = "An Analysis of the Loop Optimization Scores in {Knuth's}
`Empriical Study of {FORTRAN} Programs'",
journal = "Software---Practice and Experience",
volume = "3",
pages = "161--169",
kwds = "loop optimization, fortran"
}
@incollection{hoag:77,
author = "D. C. Hoaglin",
year = "1977",
title = "Mathematical Software and Exploratory Data Analysis",
booktitle = "Mathematical Software III",
editor = "J. Rice",
publisher = "Academic Press ",
address = "New York",
kwds = "stat, software, exploratory data analysis"
}
@article{host:72,
author = "L. L. Hoberrock and G. W. Stewart",
year = "1972",
title = "Input Requirements and Parametric Errors for Systems
Identification under Periodic Excitement",
journal = "Transactions of the AMSE",
volume = "94",
pages = "296--302",
kwds = "la, control, identifiability"
}
@article{hock:76,
author = "R. R. Hocking",
year = "1976",
title = "The Analysis and Selection of Variables in Linear Regression",
journal = "Biometrics",
volume = "32",
pages = "1-49",
kwds = "stat, regr, variable selection"
}
@article{hock:65,
author = "R. W. Hockney",
year = "1965",
title = "A Fast Direct Solution of {P}oisson's Equation Using
{F}ourier Analysis",
journal = "Journal of the {ACM}",
volume = "12",
pages = "95--113",
note = "Cited in \cite{govl:89}.",
kwds = "nla, direct Poisson solver, FFT"
}
@article{hock:83,
author = "R. Hockney",
year = "1983",
title = "Characterizing Computers and Optimizing the {FACR($\ell$)}
{P}oisson Solver on Parallel Unicomputers",
journal = "{IEEE} Transactions on Computers",
volume = "C-32",
pages = "933--941",
note = "Cited in \cite{govl:89}.",
kwds = "nla, cs, direct Poisson solver, prll"
}
@book{hoje:81,
author = "R. W. Hockney and C. R. Jesshope",
year = "1981",
title = "Parallel Computers",
publisher = "Adam Hilger Ltd.",
address = "Bristol",
kwds = "book, prll, vect, architecture"
}
@article{hock:85,
author = "R. W. Hockney",
year = "1985",
title = "{\sc Mimd} Computing in the {\sc usa}---1984",
journal = "Parallel Computing",
volume = "3",
pages = "119-136",
kwds = "prll, architecture, MIMD"
}
@article{homo:72,
author = "S. D. Hodges and P. G. Moore",
year = "1972",
title = "Data Uncertainties and Least Squares Regression",
journal = "Applied Statistics",
volume = "21",
pages = "185-195",
kwds = "stat, regr, eriv, pert"
}
@unpublished{hoer:79,
author = "A. E. Hoerl",
year = "1979",
title = "Ridge Regression\,---\,1979",
note = "Manuscript. E. I. Du Pont De Nemours \& Co.",
kwds = "stat, regr, ridge regression"
}
@article{howi:53,
author = "A. J. Hoffman and H. W. Wielandt",
year = "1953",
title = "The Variation of the Spectrum of a Normal Matrix",
journal = "Duke Mathematical Journal",
volume = "20",
pages = "37-39",
kwds = "math, eig, pert, normal matrix"
}
@article{hopa:78,
author = "W. Hoffmann and B. N. Parlett",
year = "1978",
title = "A New Proof of Global Convergence for the
Tridiagonal {QL}~Allgorithm",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "929--937",
kwds = "nla, eig, QR algorithm, tridiagonal matrix, symmetric matrix"
}
@article{hoff:89,
author = "W. Hoffman",
year = "1989",
title = "Iterative Algorithms for {Gram-Schmidt} Orthogonalization",
journal = "Computing",
volume = "41",
pages = "335--348",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Gram-Schmidt algorithm, orthogonalization, qrd"
}
@book{hocr:78,
author = "R. V. Hogg and A. T. Craig",
year = "1978",
title = "Introduction to Mathematical Statistics",
publisher = "Macmillan",
address = "New York",
note = "4th Edition",
kwds = "book, stat"
}
@article{hold:1889,
author = "O. H{\"o}lder",
year = "1899",
title = " {\"Uber} einen {Mittelwertsatz}",
journal = "{G\"otting} Nachr.",
pages = "38--47",
note = "Cited in \cite{bebe:71}.",
kwds = "la, Hoelder inequality, norm"
}
@article{hofl:79,
author = "J. N. Holt and R. Fletcher",
year = "1979",
title = "An Algorithm for Constrained Non-linear Least-squares",
journal = "J. Inst. Maths. Applics.",
volume = "23",
pages = "449--463",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
@unpublished{hopa:90,
author = "Y. P. Hong and C.-T. Pan",
year = "1990",
title = "Rank-Revealing {QR} Factorizations and {SVD}",
note = "Manuscript to appear in {\it Mathemtics of
Computation.\/} Department of Mathematical Sciences,
Northern Illinois University",
kwds = "nla, qrd, svd, condition estimation"
}
@article{hopa:92,
author = "Y. P. Hong and C.-T. Pan",
year = "1992",
title = "Rank-Revealing {QR}~Factorizations and the Singular
Value Decomposition",
journal = "Mathematics of Computation",
volume = "58",
pages = "213--232",
kwds = "la, nla, qrd, rank determination, svd"
}
@phdthesis{hopp:84,
author = "P. Hoppe",
year = "1984",
title = "{Jacobi-\"ahnliche Blockverfahren zur numerischen
Behandlung des J-symmetrischen algebraischen
Eigenwertproblems}",
school = "Fachbereichs Mathematik und Informatik,
der Fernuniversit{\"a}t\,---\,Gesamthochschule\,---\,Hagen",
kwds = "nla, eig, Jacobi-like, J-symmetric matrix"
}
@article{horn:50,
author = "A. Horn",
year = "1950",
title = "On the Singular Values of a Product of Completely Continuous
Operators",
journal = "Proceedings of the National Academy of Sciences",
volume = "36",
pages = "374--375",
kwds = "la, functional analysis, svd"
}
@book{hojo:85,
author = "R. A. Horn and C. R. Johnson",
year = "1985",
title = "Matrix Analysis",
publisher = "Cambridge University Press",
address = "Cambridge",
kwds = "book, la"
}
@book{hojo:91,
author = "R. A. Horn and C. R. Johnson",
year = "1991",
title = "Topics in Matrix Analysis",
publisher = "Cambridge University Press",
address = "Cambridge",
kwds = "book, la, text"
}
@article{hote:33,
author = "H. Hotelling",
year = "1933",
title = "Analysis of a Complex of Statistical Variables into Principal
Components",
journal = "Journal of Educational Psychology",
volume = "24",
pages = "417-441 and 498-520",
kwds = "stat, eig, svd, principal components, multivariate analysis"
}
@article{hote:36,
author = "H. Hotelling",
year = "1936",
title = "Relation between two Sets of Variates",
journal = "Biometrika",
volume = "28",
pages = "322-377",
kwds = "stat, geig, gsvd, canonical correlation, multivariate analysis"
}
@article{hote:40,
author = "H. Hotelling",
year = "1940",
title = "The Selection of Variates for Use in Prediction with Some
Comments on the General Problem of Nuisance Parameters",
journal = "The Annals of Mathematical Statistics",
volume = "11",
pages = "271-283",
kwds = "stat, variable selection, regr"
}
@article{hote:43,
author = "H. Hotelling",
year = "1943",
title = "Some New Methods in Matrix Calculations",
journal = "Annals of Mathematical Statistics",
volume = "14",
pages = "1-34",
kwds = "stat, nla, lud"
}
@article{hote:57,
author = "H. Hotelling",
year = "1957",
title = "Relation of the Newer Multivariate Statistical Methods to Factor
Analysis",
journal = "Br. J. Static. Psychol.",
volume = "10",
pages = "69-79",
kwds = "stat, svd, principal components, factor analysis,
multivariate analysis"
}
@article{hoyo:38,
author = "A. S. Householder and G. Young",
year = "1938",
title = "Matrix Approximation and Latent Roots",
journal = "American Mathematical Monthly",
volume = "45",
pages = "165-171",
kwds = "math, svd, matrix approximation"
}
@article{hous:55,
author = "A. S. Householder",
year = "1955",
title = "Terminating and Nonterminating Iterations for Solving
Linear Systems",
journal = "Journal of the Society for Industrial and Applied Mathematics",
volume = "3",
pages = "67--72",
kwds = "nla, linear system, iter"
}
@article{hous:58,
author = "A. S. Householder",
year = "1958",
title = "Unitary Triangularization of a Nonsymmetric Matrix",
journal = "Journal of the ACM",
volume = "5",
pages = "339-342",
kwds = "nla, qrd, Householder transformation"
}
@article{hous:58a,
author = "A. S. Householder",
year = "1958",
title = "The Approximate Solution of Matrix Problems",
journal = "Journal of the ACM",
volume = "5",
pages = "204--243",
kwds = "nla, linear system, iter"
}
@article{hoba:58,
author = "A. S. Householder and F. L. Bauer",
year = "1958",
title = "On Certain Methods for Expanding the Characteristic
Polynomial",
journal = "Numerische Mathematik",
volume = "1",
pages = "29--37",
kwds = "nla, eig, characteristic polynomial"
}
@article{hoba:60,
author = "A. S. Householder and F. L. Bauer",
year = "1960",
title = "On Certain Iterative Methods for Solving Linear Systems",
journal = "Numerische Mathematik",
volume = "2",
pages = "55--59",
kwds = "nla, linear system, iter"
}
@book{hous:64,
author = "A. S. Householder",
year = "1964",
title = "The Theory of Matrices in Numerical Analysis",
publisher = "Dover Publishing",
address = "New York",
note = "Originally published by Ginn Blaisdell.",
kwds = "book, la, nla"
}
@article{hous:66,
author = "A. S. Householder",
year = "1966",
title = "Separation Theorems for Normalizable Matrices",
journal = "Numerische Mathematik",
volume = "9",
pages = "46--50",
kwds = "la, eig, pert, diagonalizable matrix"
}
@article{hous:68,
author = "A. S. Householder",
year = "1968",
title = "Norms and the Localization of Roots of Matrices",
journal = "Bulletin of the American Mathematical Society",
volume = "74",
pages = "816--830",
kwds = "la, eig, norm, pert"
}
@article{hous:68a,
author = "A. S. Householder",
year = "1968",
title = "Moments and Characteristic Roots {II}",
journal = "Numerische Mathematik",
volume = "11",
pages = "126--128",
note = "Cited in \cite{govl:89}.",
kwds = "la, eig, pert"
}
@article{host:71,
author = "A. S. Householder and G. W. Stewart",
year = "1971",
title = "The Numerical Factorization of a Polynomial",
journal = "SIAM Review",
volume = "13",
pages = "438--446",
kwds = "nlop, polynomial"
}
@article{hous:71,
author = "A. S. Householder",
year = "1971",
title = "The {Pad\'e} Table, the {Frobenius} Identites, and the
qd~algorithm",
journal = "Linear Algebra and Its Applications",
volume = "4",
pages = "161--174",
kwds = "nlop, polynomial, Pade table, qd-algorithm, Frobenius identities"
}
@article{hous:71a,
author = "A. S. Householder",
year = "1971",
title = "Multigradients and the Zeros of Transcendental Functions",
journal = "Linear Algebra and Its Applications",
volume = "4",
pages = "175--182",
kwds = "nlop"
}
@techreport{hous:72,
author = "A. S. Householder",
year = "1972",
title = "{Schr\"oder} and {Trude}: a Historical Excursion",
institution = "Los Alamos Scientific Laboratory",
type = "Reprint",
number = "LA-DC-72-1121",
kwds = "nlop, polynomial, Schroeder, Trude, history"
}
-hp- -hq- -hr- -hs-
@inproceedings{hsly:91,
author = "S. F. Hsieh and K. J. R. Liu and K. Yao",
year = "1991",
title = "Applications of Truncated {QR}~Methods to Sinusoidal
Frequency Estimation",
booktitle = "Proceedings ICAASP-90",
publisher = "IEEE",
address = "Washington, DC",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, signal processing, qrd, rank determination"
}
@inproceedings{hsly:91a,
author = "S. F. Hsieh and K. J. R. Liu and K. Yao",
year = "1991",
title = "Comparisons of Truncated {QR}~and {SVD}~Methods for AR
Spectral Estimations",
booktitle = "SVD and Signal Processing, {II}",
editor = "R. J. Vaccaro",
pages = "403--418",
publisher = "Elsevier Science Publishers",
address = "Amsterdam",
kwds = "nla, signal processing, qrd, svd, rank determination"
}
-ht- -hu-
@article{huan:75,
author = "C. P. Huang",
year = "1975",
title = "A {Jacobi}-Type Method for Triangularizing an Arbitrary Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "566--570",
kwds = "nla, Jacobi-like, eig, nonsymmetric matrix"
}
@article{huan:78,
author = "C. P. Huang",
year = "1978",
title = "Computing Powers of Arbitrary {Hessenberg} Matrices",
journal = "Linear Algebra and Its Applications",
volume = "21",
pages = "123--134",
kwds = "nla, Hessenberg matrix, matrix powers"
}
@article{huan:81,
author = "C. P. Huang",
year = "1981",
title = "On the Convergence of the {QR} Algorithm with Origin Shifts for
Normal Matrices",
journal = "{IMA} Journal of Numerical Analysis",
volume = "1",
pages = "127--133",
note = "Cited in \cite{govl:89}.",
kwds = "nla, QR algorithm, normal matrix"
}
@book{hube:81,
author = "P. Huber",
year = "1981",
title = "Robust Statistics",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, robust estimation"
}
@article{husw:66,
author = "T. E. Hull and J. R. Swenson",
year = "1966",
title = "Tests of Probabilistic Models for Propagation of Roundoff Errors",
journal = "Communications of the {ACM}",
volume = "9",
pages = "108--113",
note = "Cited in \cite{govl:89}.",
kwds = "la, rounding error"
}
@article{hucu:62,
author = "J. R. Hurley and R. B. Cattell",
year = "1962",
title = "The {Procrustes} Program: {Direct} Rotation to Test a
Hypothesized Factor Structure",
journal = "Behavioral Science",
volume = "7",
pages = "258--262",
kwds = "la, stat, svd, matrix approximation, Procrustes problem"
}
-hv- -hw-
@book{hwbr:84,
author = "K. Hwang and F. A. Briggs",
year = "1984",
title = "Computer Architecture and Parallel Processing",
publisher = "McGraw-Hill",
address = "New York",
kwds = "book, prll, architecture"
}
@unpublished{hwly:92,
author = "T.-S. Hwang and W.-W. Lin and E. K. Yang",
year = "1992",
title = "Rank Revealing LU-Factorizations",
note = "To appear in {\it Linear Algebra and Its Applications.\/}
Citation communicated by Per Christian Hansen.",
kwds = "nla, lud, rank determination"
}
-hx- -hy- -hz- -ia- -ib- -ic- -id- -ie- -if- -ig- -ih- -ii- -ij- -ik-
@article{ikeb:79,
author = "Y. Ikebe",
year = "1979",
title = "On Inverses of {H}essenberg Matrices",
journal = "Linear Algebra and its Applications",
volume = "24",
pages = "93--97",
note = "Cited in \cite{govl:89}.",
kwds = "la, inverse matrix, Hessenberg matrix"
}
-il- -im- -in- -io- -ip-
@article{ipss:86,
author = "I. C. F. Ipsen and Y. Saad and M. Schultz",
year = "1986",
title = "Dense Linear Systems on a Ring of Processors",
journal = "Linear Algebra and its Applications",
volume = "77",
pages = "205--239",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, lud"
}
-iq- -ir- -is-
@book{ispo:87,
editor = "A. Iserles and M. J. D. Powell",
year = "1987",
title = "The State of the Art in Numerical Analysis",
publisher = "Oxford University Press",
note = "Cited in \cite{govl:89}.",
kwds = "book, na"
}
@book{iske:66,
author = "E. Issacson and H. B. Keller",
year = "1966",
title = "Analysis of Numerical Methods",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, na"
}
@book{istr:81,
author = "V. I. Istr{\u{a}}{\c{t}}escu",
year = "1981",
title = "Introduction to Linear Operator Theory",
publisher = "Marcel Decker",
address = "New York",
kwds = "book, field of values, functional analysis"
}
-it- -iu- -iv- -iw- -ix- -iy- -iz-
-ja-
@article{jaco:1845,
author = "C. G. J. Jacobi",
year = "1845",
title = "{Ueber eine neue Aufl\"osungsart der bei der Methode
der kleinsten Quadrate vorkommenden line\"aren Gleichungen}",
journal = "Astronomische Nachrichten",
volume = "22",
pages = "297--306",
kwds = "nla, lsq, eig, Jacobi's method, Jacobi iteration, linear system,
relaxation"
}
@article{jaco:1846,
author = "C. G. J. Jacobi",
year = "1846",
title = "{\"Uber ein leichtes Verfahren die in der Theorie
der S\"acul\"arst\"orungen vorkommenden Gleichungen
numerisch aufzul\"osen}",
journal = "{Journal f\"ur die reine und angewandte Mathematik}",
volume = "30",
pages = "51--s94",
kwds = "nla, eig, Jacobi's method, symmetric matrix"
}
@article{jaco:1857,
author = "C. G. J. Jacobi",
year = "1857, posthumous",
title = " {{}\"Uber eine elementare Transformation eines in Buzug
jedes von zwei Variablen-Systemen linearen
und homogenen Ausdrucks}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "53",
pages = "265-270",
kwds = "la, lud, Sylvester-Jacobi inertia theorem, history"
}
@article{jaco:1857a,
author = "C. G. J. Jacobi",
year = "1857, posthumous",
title = " {\"Uber einen algebraischen Fundamentalsatz und seine
Anwendungen}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "53",
pages = "275--280",
kwds = "la, lud"
}
@article{japh:91,
author = "W. Jalby and B. Philippe",
year = "1991",
title = "Stability Analysis and Improvement of the Block
Gram--Schmidt Algorithm",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "1058--1073",
kwds = "nla, Gram-Schmidt algorithm, qrd, block algorithm"
}
@article{jame:68,
author = "A. Jameson",
year = "1968",
title = "Solution of the Equation {$AX + XB = C$} by Inversion of
an {$M\times M$} or {$N\times N$} Matrix",
journal = "SIAM Journal on Applied Mathematics",
volume = "16",
pages = "1020--1023",
kwds = "nla, Sylvester equation, matrix equation"
}
@unpublished{jame:69,
author = "A. Jameson",
year = "1969?",
title = "Some New Methods of Solving the Equation
{$AX + XB = C$} with the Aid of Similarity Transformations",
note = "Manuscript. Vehicle Technology Department,
Grumman Aerospace Bethpage, Long Island",
kwds = "nla, Sylvester equation, matrix equation"
}
@article{jawo:77,
author = "M. Jankowski and H. Wozniakowski",
year = "1977",
title = "Iterative Refinement Implies Numerical Stability",
journal = "BIT",
volume = "17",
pages = "303--311",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, iterative refinement"
}
@article{jarr:??,
author = "P. Jarratt",
year = "19??",
title = "An Iterative Method for Locating Turning Points",
journal = "Computer Journal",
volume = "",
pages = "",
kwds = "nlop"
}
@article{jarr:68,
author = "P. Jarratt",
year = "1968",
title = "The Use of Comparison Series in Analysing Iteration
Functions",
journal = "Computer Journal",
volume = "11",
pages = "314--316",
kwds = "nlop"
}
-jb- -jc- -jd- -je-
@article{jeyo:83,
author = "K. C. Jea and D. M. Young",
year = "1983",
title = "On the Simplification of Generalized Conjugate Gradient Methods
for Nonsymmetrizable Linear Systems",
journal = "Linear Algebra and its Applications",
volume = "52/53",
pages = "399--417",
note = "Cited in \cite{govl:89}.",
kwds = "nla, nonsymmetric matrix, conjugate gradients"
}
@techreport{jenk:69,
author = "M. A. Jenkins",
year = "1969",
title = "Three-Stage Variable-Shift Iterations for the Solution
Solution of Polynomial Equations with a Posteriori Error
Bounds for the Zeros",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "138",
kwds = "nlop, polynomial"
}
@article{jeor:71,
author = "A. Jennings and D. R. L. Orr",
year = "1971",
title = "Applications of the Simultaneous Iteration Method
to Undamped Vibration Problems",
journal = "International Journal for Numerical Methods in Engineering",
volume = "3",
pages = "13--24",
kwds = "nla, geig, sparse, subspace iteration"
}
@article{jenn:73,
author = "A. Jennings",
year = "1973",
title = "Mass Condensation and Simultaneous Iteration for
Vibration Problems",
journal = "International Journal for Numerical Methods in Engineering",
volume = "6",
pages = "543--552",
kwds = "nla, geig, sparse, subspace iteration"
}
@article{jeos:74,
author = "L. S. Jennings and M. R. Osborne",
year = "1974",
title = "A Direct Error Analysis for Least Squares",
journal = "Numerische Mathematik",
volume = "22",
pages = "322--332",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, lsq"
}
@article{jest:75,
author = "A. Jennings and W. J. Stewart",
year = "1975",
title = "Simultaneous Iteration For Partial Eigensolution of
Real Matrices",
journal = "J. Inst. Math. Appl.",
volume = "15",
pages = "351--362",
kwds = "nla, sparse, eig, subspace iteration"
}
@article{jenn:77,
author = "A. Jennings",
year = "1977",
title = "Influence of the Eigenvalue Spectrum on the Convergence Rate of
the Conjugate Gradient Method",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "20",
pages = "61--72",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, eig"
}
@book{jenn:77a,
author = "A. Jennings",
year = "1977",
title = "Matrix Computation for Engineers and Scientists",
publisher = "John Wiley and Sons",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla"
}
@article{jeos:77,
author = "A. Jennings and M. R. Osborne",
year = "1977",
title = "Generalized Eigenvalue Problems for Certain Unsymmetric Band
Matrices",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "139--150",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, band matrix, nonsymmetric matrix"
}
@article{jenn:82,
author = "A. Jennings",
year = "1982",
title = "Bounds for the Singular Values of a Matrix",
journal = "IMA Journal of Numerical Analysis",
volume = "2",
pages = "459--474",
kwds = "la, svd, pert"
}
@article{jeos:74,
author = "L. S. Jennings and M. R. Osborne",
year = "1974",
title = "A Direct Error Analysis for Least Squares",
journal = "Numerische Mathematik",
volume = "22",
pages = "322--332",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, lsq"
}
@article{jeos:77,
author = "L. S. Jennings and M. R. Osborne",
year = "1977",
title = "Generalized Eigenvalue Problems for Rectangular Matrices",
journal = "J.\ Inst.\ Maths Applics",
volume = "20",
pages = "443--458",
kwds = "la, geig, matrix pencil"
}
@article{jens:72,
author = "P. S. Jensen",
year = "1972",
title = "The Solution of Large Symmetric Eigenproblems by Sectioning",
journal = "SIAM Journal on Numerical Analysis",
volume = "9",
pages = "534--545",
kwds = "nla, sparse, eig, symmetric matrix"
}
-jf- -jg- -jh- -ji-
@article{jina:88,
author = "K. G. Jinadasa",
year = "1988",
title = "Applications of the Matrix Operators vech and vec",
journal = "Linear Algebra and Its Applications",
volume = "101",
pages = "81-86",
kwds = "stat, regr, vec operator, random matrix"
}
-jj- -jk- -jl- -jm- -jn- -jo-
@article{john:73,
author = "T. L. Johnsen",
year = "1973",
title = "On the Computation of Natural Modes of an Unsupported
Vibrating Structure by Simultaneous Iteration",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "2",
pages = "305--322",
kwds = "nla, gieg, sparse, subspace iteration"
}
@article{john:73a,
author = "C. R. Johnson",
year = "1973",
title = "A {Ger\v{s}gorin} Inclusion Set for the Field of Values
of a Finite Matrix",
journal = "Proceedings of the American Mathematical Society",
volume = "41",
pages = "57--60",
kwds = "la, eig, field of values, Gerschgorin's theorem"
}
@article{jone:74,
author = "C. R. Johnson and M. Newman",
year = "1974",
title = "How Bad is the {Hadamard} Determinantal Bound?",
journal = "Journal of Research of the National Bureau of Standards",
volume = "78B",
pages = "167--169",
kwds = "la, Hadamard inequality, determinant"
}
@article{john:78,
author = "C. R. Johnson",
year = "1978",
title = "Numerical Determination of the Field of Values of
a General Complex Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "595--602",
kwds = "la, field of values"
}
@article{john:81,
author = "C. R. Johnson",
year = "1981",
title = "Row Stochastic Matrices Similar to Doubly Stochastic Matrices",
journal = "Linear and Multilinear Algebra",
volume = "10",
pages = "113--130",
kwds = "la, stochastic matrix, Markov chain, doubly stochastic matrix"
}
@article{joph:71,
author = "J. Johnson and C. L. Phillips",
year = "1971",
title = "An Algorithm for the Computation of the Integral of the State
Transition Matrix",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-16",
pages = "204--205",
note = "Cited in \cite{govl:89}.",
kwds = "nla, control"
}
@article{jomp:83,
author = "O. G. Johnson and C. A. Micchelli and G. Paul",
year = "1983",
title = "Polynomial Preconditioners for Conjugate Gradient Calculations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "20",
pages = "362--376",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning"
}
@techreport{john:84,
author = "S. L. Johnsson",
year = "1984",
title = "Odd-Even Cyclic Reduction on Ensemble Architectures and the
Solution of Tridiagonal Systems of Equations",
number = "YALEU DCS RR-339",
institution = "Computer Science, Yale University",
address = "New Haven, CT",
note = "Cited in \cite{govl:89}.",
kwds = "nla, cyclic reduction, tridiagonal matrix, linear system"
}
@article{john:85,
author = "S. L. Johnsson",
year = "1985",
title = "Solving Narrow Banded Systems on Ensemble Architectures",
journal = "{ACM} Transactions on Mathematical Software",
volume = "11",
pages = "271--288",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, band matrix"
}
@incollection{john:86,
author = "S. L. Johnsson",
year = "1986",
title = "Band Matrix System Solvers on Ensemble Architectures",
booktitle = "Supercomputers: Algorithms, Architectures, and Scientific
Computation",
editor = "F. A. Matsen and T. Tajima",
publisher = "University of Texas Press",
address = "Austin, TX",
pages = "196--216",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, band matrix"
}
@techreport{joho:86,
author = "S. L. Johnsson and C.-T. Ho",
year = "1986",
title = "Spanning Graphs for Optimum Broadcasting
and Personalized Communication in Hypercubes",
institution = "Department of Computer Science,
Yale University",
type = "Research Report",
number = "YALE/DCS/RR-500",
kwds = "prll, hypercube, communication"
}
@techreport{john:87,
author = "S. L. Johnsson",
year = "1987",
title = "The {FFT} and Fast {Poisson} Solvers on Parallel
Architectures",
institution = "Department of Computer Science,
Yale University",
type = "Technical Report",
number = "YALE/DCS/TR-582",
kwds = "prll, fft, fast algorithm, direct Poisson solver"
}
@article{john:87a,
author = "S. L. Johnsson",
year = "1987",
title = "Solving Tridiagonal Systems on Ensemble Architectures",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "8",
pages = "354--392",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, tridiagonal matrix"
}
@article{john:87b,
Author = "S. L. Johnsson",
year = "1987",
title = "Communication Efficient Basic Linear Algebra Computations on
Hypercube Multiprocessors",
journal = "Journal of Parallel and Distributed ",
volume = "4",
pages = "133--172",
note = "Cited in \cite{govl:89}.",
kwds = "nla, blas, prll, hypercube"
}
@techreport{joho:87,
author = "S. L. Johnsson and C.-T. Ho",
year = "1987",
title = "Matrix Multiplication on {Boolean} Cubes Using
Generic Communication Primitives",
institution = "Department of Computer Science,
Yale University",
type = "Research Report",
number = "YALE/DCS/RR-530",
kwds = "nla, prll, hypercube, matrix multiplication, communication"
}
@techreport{joho:87a,
author = "S. L. Johnsson and C.-T. Ho",
year = "1987",
title = "Multiple Tridiagonal Systems, the Alternating
Direction Methods and {Boolean} Cube Configured
Multiprocessors",
institution = "Department of Computer Science,
Yale University",
type = "Technical Report",
number = "YALEU/DCS/TR-532",
kwds = "nla, prll, hypercube, tridiagonal matrix, alternating direction,
communication"
}
@techreport{jhjr:87c,
author = "S. L. Johnsson and C.-T. Ho and
M. Jacquemin and A. Ruttenberg",
year = "1987",
title = "Computing Fast {Fourier} Transfroms on Boolean
Cubes and Related Networks",
institution = "Department of Computer Science,
Yale University",
type = "Technical Report",
number = "YALE/DCS/TR-598",
kwds = "prll, fft, fast algorithm, hypercube, communication"
}
@article{joho:88,
author = "S. L. Johnsson and C. T. Ho",
year = "1988",
title = "Algorithms for Matrix Transposition on {B}oolean {$N$}-Cube
Configured Ensemble Architectures",
journal = "{SIAM} Journal on Matrix Analysis and Applications",
volume = "9",
pages = "419--454",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, hypercube, matrix transpose"
}
@book{john:72,
author = "J. Johnston",
year = "1972",
title = "Econometric Methods",
publisher = "Mc Graw-Hill",
address = "New York",
edition = "2nd",
kwds = "book, stat, econometrics, regr"
}
@article{john:71,
author = "R. L. Johnston",
year = "1971",
title = "{G}ershgorin Theorems for Partitioned Matrices",
journal = "Linear Algebra and its Applications",
volume = "4",
pages = "205--220",
note = "Cited in \cite{govl:89}.",
kwds = "la, Gerschgorin's theorem, block matrix"
}
@book{jord:1870,
author = "C. Jordan",
year = "1870",
title = "Trait{\'e} des Substitutions et des {\'E}quations
{A}lg\-{\'e}briques",
publisher = "",
address = "Paris",
note = "Cited in \cite{macd:46}.",
kwds = "book, la, Jordan form"
}
@article{jord:1874,
author = "C. Jordan",
year = "1874",
title = "M\'emoire sur les formes bilin\'eaires",
journal = "Journal de Math\'ematiques Pures et Appliqu\'ees, Deuxi\`eme
S\'erie",
volume = "19",
pages = "35-54",
kwds = "la, svd, geig"
}
@article{jord:1874a,
author = "C. Jordan",
year = "1874",
title = "Sur la r\'eduction des formes bilin\'eaires",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "78",
pages = "614--617",
kwds = "la, svd, geig"
}
@article{jord:1875,
author = "C. Jordan",
year = "1875",
title = "Essai sur la g\'eom\'etrie \`a n dimensions",
journal = "Bulletin de la Soci\'et\'e Math\'ematique",
volume = "3",
pages = "103-174",
kwds = "la, gsvd, canonical angles"
}
@article{jord:87,
author = "H. Jordan",
year = "1987",
title = "Interpreting Parallel Processor Performance Measurements",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "8",
pages = "s220--s226",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll"
}
@article{jovn:35,
author = "P. Jordan and von Neumann, J.",
year = "1935",
title = "On Inner Products in Linear Metric Spaces",
journal = "Annals of Mathematics",
volume = "36",
pages = "719--723",
kwds = "la, norm, rhombus rule"
}
@article{jord:68,
author = "T. L. Jordan",
year = "1968",
title = "Experiments on Error Growth Associated with some Linear
Least-squares Procedures",
journal = "Mathematics of Computation",
volume = "22",
pages = "579--588",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, Gram-Schmidt algorithm"
}
@inproceedings{jord:84,
author = "T. Jordan",
year = "1984",
title = "Conjugate Gradient Preconditioners for Vector and Parallel
Processors",
booktitle = "Proceedings of the Conference on Elliptic Problem Solvers",
editor = "G. Birkoff and A. Schoenstadt",
publisher = "Academic Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vect, prll, conjugate gradients,
preconditioning"
}
-jp- -jq- -jr- -js- -jt- -ju- -jv- -jw- -jx- -jy- -jz-
-ka-
@article{kacz:37,
author = "S. Kaczmarz",
year = "1937",
title = "{\"Angen\"aherte Aufl\"osung von Systemen linearer
Gleichungen}",
journal = "Bull. Internat. Acad. Polon. Sci. Cl. A.",
volume = "",
pages = "355--356",
note = "Cited in \cite{hous:64}",
kwds = "nla, Kaczmarz's method, projection method, linear system"
}
@article{kada:71,
author = "J. B. Kadane",
year = "1971",
title = "Comparison of $k$-Class Estimators When the
Disturbances are Small",
journal = "Econometrica",
volume = "39",
pages = "723--737",
kwds = "stat, regr, eriv"
}
@article{kags:77,
author = "B. K{\aa}gstr{\"o}m",
year = "1977",
title = "Bounds and Perturbation Bounds for the Matrix Exponential",
journal = "BIT",
volume = "17",
pages = "39--57",
kwds = "la, pert, matrix exponential, matrix function"
}
@techreport{kags:77a,
author = "B. K{\aa}gstr{\"o}m",
year = "1977",
title = "Numerical Computation of Matrix Functions",
number = "UMINF-58.77",
institution = "Information Processing, University of Ume{\aa}",
address = "Ume{\aa}, Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function"
}
@article{karu:80,
author = "B. K{\aa}gstr{\"o}m and A. Ruhe",
year = "1980",
title = "An Algorithm for Numerical Computation of the
{Jordan} Normal Form of a Complex Matrix",
journal = "Transactions on Mathematical Software",
volume = "6",
pages = "398-419",
kwds = "nla, eig, Jordan form, software"
}
@article{karu:80a,
author = "B. K{\aa}gstr{\"o}m and A. Ruhe",
year = "1980",
title = "Algorithm 560: {JNF}, An Algorithm for Numerical
Computation of the {Jordan} Normal Form of a Complex Matrix",
journal = "Transactions on Mathematical Software",
volume = "6",
pages = "437--443",
kwds = "nla, eig, Jordan form, software"
}
@proceedings{karu:83,
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
year = "1983",
title = "Proceedings of the Conference on Matrix Pencils,
{P}ite {H}avsbad 1982",
series = "Lecture Notes in Mathematics",
volume = "973",
publisher = "Springer-Verlag",
address = "New York and Berlin",
note = "Cited in \cite{govl:89}.",
kwds = "la, nla, gieg"
}
@article{kags:85,
author = "B. K{\aa}gstr{\"o}m",
year = "1985",
title = "The Generalized Singular Value Decomposition and the General
{$A - \lambda B$} Problem",
journal = "{BIT}",
volume = "24",
pages = "568--583",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, gsvd"
}
@article{kags:86,
author = "B. K{\aa}gstr{\"o}m",
year = "1986",
title = "{RGSVD}---An Algorithm for Computing the {Kronecker} Structure
and Reducing Subspaces of Singular {$A-\lambda B$}
Pencils",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "185--211",
kwds = "nla, geig, Kronecker form, reducing subspace, matrix pencil"
}
@techreport{kanp:87,
author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa",
year = "1987",
title = "Parallel Algorithms for Solving the Triangular {S}ylvester Equation
on a Hypercube Multiprocessor",
number = "UMINF-136.87",
institution = "Information Processing, University of Ume{\aa}",
address = "S-901 87 Ume{\aa}, Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Sylvester equation, triangular matrix, prll, hypercube,
matrix equation"
}
@techreport{kawe:87,
author = "B. K{\aa}gstr{\"o}m and L. Westin",
year = "1987",
title = "Generalized {Schur} Methods with Condition Estimators for
the Generalized {Sylvester} Equation",
institution = "Institute of Information Processing,
University of Ume{\aa}",
type = "Report",
number = "UMINF-130.86",
kwds = "nla, Schur form, Sylvester equation, matrix equation, geig, pert"
}
@techreport{kawe:87a,
author = "B. K{\aa}gstr{\"o}m and L. Westin",
year = "1987",
title = "{GSYLV}---Fortran Routines for the Generalized
{Schur} Method with $\rm dif^{-1}$-estimators for
Solving the Generalized {Sylvester} Equation",
institution = "Institute of Information Processing,
University of Ume{\aa}",
type = "Report",
number = "UMINF-132.86",
kwds = "nla, Schur form, Sylvester equation, geig, pert,
matrix equation, software"
}
@techreport{kali:88,
author = "B. K{\aa}gstr{\"o}m and P. Ling",
year = "1988",
title = "Level 2 and 3 {BLAS} Routines for the {IBM 3090 VF/400}:
Implementation and Experiences",
number = "UMINF-154.88",
institution = "Information Processing, University of Ume{\aa}",
address = "S-901 87 Ume{\aa}, Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, blas"
}
@techreport{kanp:88,
author = "B. K{\aa}gstr{\"o}m and L. Nystr{\"o}m and P. Poromaa",
year = "1988",
title = "Parallel Shared Memory Algorithms for Solving the Triangular
{S}ylvester Equation",
number = "UMINF-155.88",
institution = "Information Processing, University of Ume{\aa}",
address = "S-901 87 Ume{\aa}, Sweden",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Sylvester equation, triangular matrix, prll, hypercube,
matrix equation"
}
@article{kaha:66,
author = "W. Kahan",
year = "1966",
title = "Numerical Linear Algebra",
journal = "Canadian Mathematical Bulletin",
volume = "9",
pages = "757--801",
kwds = "nla, condition"
}
@techreport{kaha:66a,
author = "W. Kahan",
year = "1966",
title = "When to Neglect Off-Diagonal Elements of Symmetric
Tri-Diagonal Matrices",
institution = "Computer Science Department, Stanford Univeristy",
type = "Technical Report",
number = "CS42",
kwds = "la, nla, pert, eig, tridiagonal matrix, symmetric matrix"
}
@techreport{kaha:66b,
author = "W. Kahan",
year = "1966",
title = "Relaxations Methods for an Eigenproblem",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS44",
kwds = "nla, geig, relaxation"
}
@techreport{kaha:67,
author = "W. Kahan",
year = "1967",
title = "Inclusion Theorems for Clusters of Eigenvalues
of {Hermitian} Matrices",
institution = "Computer Science Department, University of
Toronto",
type = "Technical Report",
number = "",
kwds = "la, eig, pert, residual bound, symmetric matrix"
}
\@article{kaha:67a,
author = "W. Kahan",
year = "1967",
title = "{Laguerre's} Method and a Circle Which Contains at Least
One Zero of a Polynomial",
journal = "SIAM Journal on Numerical Analysis",
volume = "4",
pages = "474--482",
kwds = "nlop, polynomial, Laguerre's method, pert"
}
@article{kaha:68,
author = "W. Kahan",
year = "1968",
title = "Circumscribing an Ellipsoid about the Intersection of Two
Ellipsoids",
journal = "Canadian Mathematical Bulletin",
volume = "11",
pages = "437--441",
kwds = "la, field of values, ellipsoid"
}
@techreport{kaha:72,
author = "W. Kahan",
year = "1972",
title = "Conserving Confluence Curbs Ill-Conditioning",
institution = "Computer Science Department,
University of California, Berkeley",
type = "Technical Report",
number = "6",
kwds = "nla, ill-conditioned problem, rank determination, regularization"
}
@article{kaha:73,
author = "W. Kahan",
year = "1973",
title = "Every $n\times n$ Matrix {$Z$} with Real Spectra
Satisfies {$\|Z-Z^*\|\leq \|Z+Z^*\|(\log n + 0.038)$}",
journal = "Proceedings of the American Mathematical Society",
volume = "39",
pages = "235--241",
kwds = "la, eig, norm"
}
@unpublished{kaha:73a,
author = "W. Kahan",
year = "1973",
title = "The Field of Values of the {Gauss} Transform",
note = "Handwritten Manuscript",
kwds = "la, eig, Schur complement, field of values"
}
@techreport{kapa:74,
author = "W. Kahan and B. Parlett",
year = "1974",
title = "An Analysis of {Lanczos} Algorithms for Symmetric Matrices",
institution = "Electronics Research Laboratory, University of
California, Berkeley",
type = "Memorandum",
number = "ERL-M467",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix"
}
@article{kaha:75,
author = "W. Kahan",
year = "1975",
title = "Spectra of Nearly {Hermitian} Matrices",
journal = "Proceedings of the American Mathematical Society",
volume = "48",
pages = "11--17",
kwds = "la, eig, pert, symmetric matrix"
}
@incollection{kapa:76,
author = "W. Kahan and B. N. Parlett",
year = "1976",
title = "How Far Should You Go with the {L}anczos Process?",
booktitle = "Sparse Matrix Computations",
editor = "J. Bunch and D. Rose",
publisher = "Academic Press",
address = "New York",
pages = "131--144",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm"
}
@article{kaha:79,
author = "W. Kahan",
year = "1979",
title = "Personal Calculator Has Key to Solve Any Equation
$f(x)=0$",
journal = "Hewlett--Packard Journal",
volume = "30",
pages = "20--26",
kwds = "nlop"
}
@article{kaha:80,
author = "W. Kahan",
year = "1980",
title = "Handheld Calculator Evaluates Integral",
journal = "Hewlett--Packard Journal",
volume = "31",
pages = "23--32",
kwds = "na, numerical integration"
}
@unpublished{kaha:81,
author = "W. Kahan",
year = "1981",
title = "Why Do We Need a Floating-Point Standard",
note = "Manuscript. University of California, Berkeley",
kwds = "na, rounding error, computer arithmetic"
}
@techreport{kaha:82,
author = "W. Kahan",
year = "1982",
title = "Branch Cuts for Complex Elementary Functions",
institution = "Center for Pure and Applied Mathematics,
University of California, Berkeley",
type = "Technical Report",
number = "PAM-105",
kwds = "na, elementary function"
}
@article{kapj:82,
author = "W. Kahan and B. N. Parlett and E. Jiang",
year = "1982",
title = "Residual Bounds on Approximate Eigensystems
of Nonnormal Matrices",
journal = "SIAM Journal on Numerical Analysis",
volume = "19",
pages = "470-484",
kwds = "math, la, nla, pert, eig, backward perturbation, nonsymmetric matrix"
}
@inproceedings{kaco:82,
author = "W. Kahan and J. T. Coonen",
year = "1982",
title = "The Near Orthogonality of Syntax, Semantics, and
Diagnostics in Numerical Programming Environments",
booktitle = "The Relationship Between Numerical Computation
and Programming Languages",
editor = "J. K. Reid",
pages = "103--115",
publisher = "North-Holland",
address = "",
kwds = "na, rounding error, programming environment"
}
@inproceedings{kavm:??,
author = "T. Kailath and A. Vieira and M. Morf",
year = "19??",
title = "Inverses of {Toeplitz} Operators, Innovations, and Orthogonal
Polynomials",
booktitle = "",
editor = "",
pages = "",
publisher = "",
address = "",
kwds = "nla, Toeplitz matrix, orthogonal polynomial, fast algorithm,
inverse matrix"
}
@article{kakm:79,
author = "T. Kailath and S.-Y. Kung and M. Morf",
year = "1979",
title = "Displacement Ranks of a Matrix",
journal = "Bulletin of the American Mathematical Society",
volume = "1",
pages = "769--773",
kwds = "nla, Toeplitz matrix, fast algorithm"
}
@article{kasa:89,
author = "C. Kamath and A. Sameh",
year = "1988/89",
title = "A Projection Method for Solving Nonsymmetric Linear Systems on
Multiprocessors",
journal = "Parallel Computing",
volume = "9",
pages = "291--312",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, nonsymmetric matrix, linear system, projection method"
}
@article{kava:72,
author = "W. J. Kammerer and R. S. Varga",
year = "1972",
title = "On Asymptotically Best Norms for Powers of Operators",
journal = "Numerische Mathematik",
volume = "20",
pages = "93--98",
kwds = "la, norm, matrix powers"
}
@article{kana:72,
author = "W. J. Kammererer and M. Z. Nashed",
year = "1972",
title = "On the Convergence of the Conjugate Gradient Method for
Singular Linear Operator Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "9",
pages = "165--181",
kwds = "nla, conjugate gradients, singular matrix"
}
@article{kani:66,
author = "S. Kaniel",
year = "1966",
title = "Estimates for Some Computational Techniques in
Linear Algebra",
journal = "Mathematics of Computation",
volume = "20",
pages = "369--378",
kwds = "nla, eig, pert, Lanczos algorithm, symmetric matrix"
}
@article{kabr:84,
author = "R. N. Kapur and J. C. Browne",
year = "1984",
title = "Techniques for Solving Block Tridiagonal Systems on Reconfigurable
Array Computers",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "5",
pages = "701--719",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, block triangular matrix,
linear system, prll"
}
@article{kara:74,
author = "I. Karasalo",
year = "1974",
title = "A Criterion for Truncation of the {QR} Decomposition Algorithm
for the Singular Linear Least Squares Problem",
journal = "BIT",
volume = "14",
pages = "156--166",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition, rank determination, qrd"
}
@book{kata:75,
author = "S. Karlin and H. M. Taylor",
year = "1975",
title = "A First Course in Stochastic Processes",
edition = "Second",
publisher = "Academic Press",
address = "New York",
kwds = "book, math, probability, stochastic process"
}
@techreport{karl:90,
author = "R. Karlson",
year = "1990",
title = "A Study of Some Roundoff Effects of the
{GMRES}-Method",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-Mat-R-1990-11",
kwds = "nla, linear system, gmres"
}
@techreport{kasw:92,
author = "R. Karlsson and J.-G. Sun and B. Wald\`en",
year = "1992",
title = "Optimal Backward Perturbation Bounds for the Linear Least
Squares Problem",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MAT-R-1992-06",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "la, pert, backward perturbation, lsq"
}
@article{kami:66,
author = "R. Karp and R. Miller",
year = "1966",
title = "Properties of a Model for Parallel Computation:
Determinacy, Termination, Queuing",
journal = "SIAM Journal on Applied Mathematics",
volume = "14",
pages = "1390-1411",
kwds = "prll, determinacy"
}
@unpublished{kagr:86,
author = "A. H. Karp and J. Greenstadt",
year = "1986",
title = "An Improved Parallel {Jacobi} Method for Diagonalizing
a Symmetric Matrix",
note = "Manuscript. IBM Scientific Center, Palo Alto, CA",
kwds = "nla, prll, eig, Jacobi's method, symmetric matrix"
}
@article{karu:51,
author = "W. Karush",
year = "1951",
title = "An Iterative Method for Finding Characteristic
Vectors of a Symmetric Matrix",
journal = "Pacific Journal of Mathematics",
volume = "1",
pages = "233--248",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix, sparse"
}
@book{kato:66,
author = "T. Kato",
year = "1966",
title = "Perturbation Theory for Linear Operators",
publisher = "Springer Verlag",
address = "New York",
kwds = "book, la, eig, pert, functional analysis"
}
@article{kauf:74,
author = "L. Kaufman",
year = "1974",
title = "The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "997--1024",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, LZ algorithm"
}
@article{kauf:75,
author = "L. Kaufman",
year = "1975",
title = "Variable Projection Methods for Solving Separable Nonlinear
Least Squares Problems",
journal = "BIT",
volume = "15",
pages = "49--57",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{kauf:77,
author = "L. Kaufman",
year = "1977",
title = "Some Thoughts on the {QZ} Algorithm for Solving the Generalized
Eigenvalue Problem",
journal = "{ACM} Transactions on Mathematical Software",
volume = "3",
pages = "65--75",
note = "Cited in \cite{govl:89}.",
kwds = "nla, gieg, QZ algorithm"
}
@article{kape:78,
author = "L. Kaufman and V. Pereyra",
year = "1978",
title = "A method for Separable Nonlinear Least Squares Problems with
Separable Nonlinear Equality Constraints",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "12--20",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
@article{kauf:79,
author = "L. Kaufman",
year = "1979",
title = "Application of Dense {Householder} Transformation
to a Sparse Matrix",
journal = "ACM Transactions on Mathematical Software",
volume = "5",
pages = "442--450",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, Householder transformation, sparse"
}
@article{kauf:83,
author = "L. Kaufman",
year = "1983",
title = "Matrix Methods for Queuing Problems",
journal = "SIAM J. on Scientific and Statistical Computing",
volume = "4",
pages = "525--552",
kwds = "nla, queue, Markov chain, lud, relaxation"
}
@article{kauf:87,
author = "L. Kaufman",
year = "1987",
title = "The Generalized {Householder} Transformation and Sparse Matrices",
journal = "Linear Algebra and Its Applications",
volume = "90",
pages = "221--234",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, Householder transformation, qrd"
}
@article{kago:83,
author = "J. Kautsky and G. H. Golub",
year = "1983",
title = "On the Calculation of {J}acobi Matrices",
journal = "Linear Algebra and its Applications",
volume = "52/53",
pages = "439--456",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi matrix"
}
-kb- -kc- -kd- -ke-
@article{kell:65,
author = "H. B. Keller",
year = "1965",
title = "On the Solution of Singular and Semidefinite Linear
Systems by Iteration",
journal = "SIAM Journal on Numerical Analysis",
volume = "2",
pages = "281--290",
kwds = "nla, linear system, iter, singular system"
}
@article{kell:65,
author = "J. Keller",
year = "1965",
title = "On the Solution of Singular and Semidefinite Linear Systems
by Iterations",
journal = "SIAM Journal, Ser. B ",
volume = "2",
pages = "281--290",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, iter, ginv, linear system"
}
@article{kend:51,
author = "D. G. Kendall",
year = "1951",
title = "Some Problems in the Theory of Queues",
journal = "Journal of the Royal Statistical Society (B)",
volume = "13",
pages = "151-173 and 184-185",
kwds = "queue"
}
@article{kend:53,
author = "D. G. Kendall",
year = "1953",
title = "Stochastic Processes Occuring in the Theory of Queues and their
Analysis by the Method of the Imbedded {Markov} Chain",
journal = "Annals of Mathematical Statistics",
volume = "24",
pages = "338-354",
kwds = "la, queue, Markov chain"
}
@book{kege:80,
author = "W. J. Kennedy and J. E. Gentle",
year = "1980",
title = "Statistical Computing",
publisher = "Marcel Dekker",
address = "New York",
kwds = "book, stat, na"
}
@unpublished{kezi:89?,
author = "K. Kennedy and H. P. Zima",
year = "1989?",
title = "Virtual Shared Memory for Distributed Memory Machines",
note = "Undated manuscript, Rice University.",
kwds = "cs, prll, shared memory, distributed memory"
}
@article{kela:88,
author = "C. Kenney and A. J. Laub",
year = "1988",
title = "Controllability and Stability Radii for Companion
Form Systems",
journal = "Mathematics of Control Signals and Systems",
volume = "1",
pages = "239--256",
kwds = "nla, controllability, stability, companion matrix, svd"
}
@article{kelw:89,
author = "C. Kenney and A. J. Laub and M. Wette",
year = "1989",
title = "A Stability-Enhancing Scaling Procedure for {Schur--Riccati}
Solvers",
journal = "Systems \& Control Letters",
volume = "12",
pages = "241--250",
kwds = "nla, Riccati equation, pert, scaling"
}
@article{kela:89,
author = "C. Kenney and A. J. Laub",
year = "1989",
title = "Condition Estimates for Matrix Functions",
journal = "SIAM Journal of Matrix Analysis and Applications",
volume = "10",
pages = "191--209",
kwds = "la, pert, matrix function"
}
@incollection{kers:82,
author = "D. Kershaw",
year = "1982",
title = "Solution of Single Tridiagonal Linear Systems and Vectorization of
the {ICCG} Algorithm on the {C}ray-1",
booktitle = "Parallel Computation",
editor = "G. Roderigue",
publisher = "Academic Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, vect, tridiagonal matrix"
}
-kf- -kg- -kh-
@article{khac,
author = "L. C. Kha\v{c}iyan",
year = "1979",
title = "Polynomial Algorithm for Linear Programming",
journal = "Soviet Doklady",
volume = "244",
pages = "1093--1096",
note = "Typed translation",
kwds = "nlop, linear programming"
}
@article{khgo:89,
author = "A. I. Khuiri and I. J. Good",
year = "1989",
title = "The Parameterization of Orthogonal Matrices:
{A} Review Mainly for Statisticians",
journal = "South African Statistical Journal",
volume = "23",
pages = "231--250",
kwds = "stat, orthogonal matrix, random matrix"
}
-ki-
@article{kiel:87,
author = "A. Kielbasinski",
year = "1987",
title = "A Note on Rounding Error Analysis of {C}holesky Factorization",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "487--494",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, Cholesky decomposition"
}
@article{kiap:90,
author = "S. Kim and D. P. Agrawal and R. J. Plemmons",
year = "1990",
title = "Least-Squares Updating Algorithms on a Hypercube",
journal = "Journal of Parallel and Distrubuted Computing",
volume = "8",
pages = "80--88",
kwds = "nla, lsq, updating, hypercube, prll"
}
@article{kinc:73,
author = "D. R. Kincaid",
year = "1973",
title = "A Class of Norms of Iterative Methods for Solving
Systems of Linear Equations",
journal = "Numerische Mathematik",
volume = "20",
pages = "392--408",
kwds = "nla, linear system, norm, iter"
}
@article{king:76,
author = "R. F. King",
year = "1976",
title = "Methods Without Secant Steps for Finding a Bracket Root",
journal = "Computing",
volume = "17",
pages = "49--57",
kwds = "nlop, secant method"
}
@article{king:77,
author = "R. F. King",
year = "1977",
title = "A Secant Method for Multiple Roots",
journal = "BIT",
volume = "17",
pages = "321--328",
kwds = "nlop, secant method, multiple zero"
}
@article{king:79,
author = "R. F. King",
year = "1979",
title = "An Extrapolation Method of Order Four for
Linear Sequences",
journal = "Siam Journal on Numerical Analysis",
volume = "5",
pages = "719--725",
kwds = "nlop, extrapolation"
}
@article{king:80,
author = "R. F. King",
year = "1980",
title = "An Effecient One-Point Extrapolation Method for
Linear Convergence",
journal = "Mathematics of Computation",
volume = "35",
pages = "1285--1290",
kwds = "nlop, extrapolation"
}
@article{kiou:79,
author = "J. B. Kioustelidis",
year = "1979",
title = "A Derivative-Free Transformation Preserving the
Order of Convergenc of Iteration Methods in Case of
Multiple Zeros",
journal = "Numerische Mathematik",
volume = "15",
pages = "385--389",
kwds = "nlop, Newton's method, multiple zero"
}
-kj- -kk- -kl-
@article{klee:62,
author = "V. Klee",
year = "1962",
title = "Review of `Linearity of Best Approximations: A Characterization
of Ellipsoids' ({Rudin} and {Smith})",
journal = "Math Reviews",
volume = "23",
pages = "A2028",
kwds = "math, ginv, best approximation"
}
@book{klei:75,
author = "L. Kleinrock",
year = "1975",
title = "Queueing Systems. Volume I: Theory",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, queue, Markov chain"
}
@book{klei:76,
author = "L. Kleinrock",
year = "1976",
title = "Queueing Systems. Volume II: Computer Applications",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, queue, Markov chain"
}
@book{klin:72,
author = "M. Kline",
year = "1972",
title = "Mathematical Thought from Ancient to Modern Times",
publisher = "Oxford University Press",
address = "New York",
kwds = "book, math, history"
}
-km- -kn-
@article{knau:71,
author = "B. Knauer",
year = "1971",
title = "{Untere Schranken f\"ur die Eigenwerte selbstadjungierter
positiv-definiter Operatoren}",
journal = "Numerische Mathemetik",
volume = "17",
pages = "166--171",
kwds = "la, eig, pert, symmetric matrix, functional analysis"
}
@unpublished{knut:71,
author = "D. E. Knuth",
year = "1971",
title = "The Dangers of Computer-Science Theory",
note = "May have appeared in IFIP 71, Ljubijana. Manuscript",
kwds = "cs"
}
@article{knut:74,
author = "D. E. Knuth",
year = "1974",
title = "Structured Programmin with go to Statements",
journal = "Computing Surveys",
volume = "6",
pages = "261-301",
kwds = "structured programming"
}
@article{knya:87,
author = "A. V. Knyazev",
year = "1987",
title = "Convergence Rate Estimate for Iterative Methods for
a Mesh Symmetric Eigenvalue Problem",
journal = "Sov.~J. Numer.\ Anal.\ Math.\ Modelling",
volume = "2",
pages = "371--396",
note = "Originally published in Russian in {\it Numerical Methods
and Mathematical Modelling,\/} Transactions of the Department
of Numerical Mathematics of the USSR Academy of Sciences,
Moscow, 1986.",
kwds = "nla, geig"
}
-ko-
@article{kogb:55,
author = "E. G. Kogbetliantz",
year = "1955",
title = "Solution of Linear Systems by Diagonalization of
Coefficients Matrix",
journal = "Quarterly of Applied Mathematics",
volume = "13",
pages = "123--132",
kwds = "nla, Kogbetliantz's algorithm, svd"
}
@article{koen:16,
author = "D. K{\"o}nig",
year = "1916",
title = "{\"Uber Graphen und ihre Anwendung auf Determinantentheorie
und Mengenlehre}",
journal = "Mathematische Annalen",
volume = "77",
pages = "453--465",
kwds = "la, Koenig-Frobenius theorem, determinant"
}
@article{koni:81,
author = "H. S. Konijn",
year = "1981",
title = "Maximum Likelihood Estimators and Confidence Intervals for a
Simple Errors in Variables Model",
journal = "Communications in Statistics: Part A",
volume = "10",
pages = "983-996",
kwds = "stat, regr, eriv, confidence interval"
}
@article{koya:88,
author = "K. Konstantinides and K. Yao",
year = "1988",
title = "Statistical Analysis of Effective Singular Values
in Matrix Rank Determination",
journal = "IEEE Transactions on Acoustics, Speech, and Signal Processing",
volume = "36",
pages = "757--763",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, svd, random matrix, rank determination"
}
@unpublished{kops:90,
author = "K. Kontovasilis and R. J. Plemmons and W. J. Stewart",
year = "1990",
title = "{P}-Cyclic {SOR} for {Markov} chains",
note = "Manuscript. Department of Mathematics and Computer Science,
Wake Forest University",
kwds = "nla, Markov chain, iter, relaxation, eig"
}
@article{koms:84,
author = "J. R. Koury and D. F. McAllister and W. J. Stewart",
year = "1984",
title = "Iterative Methods for Computing the Stationary
Distribution of Nearly Completely Decomposable {Markov}
Chains",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "5",
pages = "164--185",
kwds = "nla, Markov chain, nearly uncoupled system, iter"
}
@article{kopa:81,
author = "S. Kourouklis and C. C. Paige",
year = "1981",
title = "A Constrained Approach to the General {Gauss-Markov} Linear Model",
journal = "Journal of the American Statistical Association",
volume = "76",
pages = "620-625",
kwds = "stat, nla, regr, generalized linear model, constraints, lsq"
}
@article{kova:70,
author = "Z. V. Kovarik",
year = "1970",
title = "Some Iterative Methods for Improving Orthonormality",
journal = "SIAM Journal on Numerical Analysis",
volume = "7",
pages = "386--389",
kwds = "nla, orthogonalization, projection"
}
@article{kova:74,
author = "Z. V. Kovarik",
year = "1974",
title = "Spectrum Localization in {Banach} Space {I}",
journal = "Linear Algebra and Its Applications",
volume = "8",
pages = "225--236",
kwds = "la, pert, eig, Gerschgorin's theorem, functional analysis"
}
@article{kova:75,
author = "Z. V. Kovarik",
year = "1975",
title = "Spectrum Localization in {Banach} Space {II}",
journal = "Linear Algebra and Its Applications",
volume = "12",
pages = "223--229",
kwds = "la, pert, eig, Gerschgorin's theorem, functional analysis"
}
@article{kova:77,
author = "Z. V. Kovarik",
year = "1977",
title = "Similarity and Interpolation Between Projectors",
journal = "Acta Scientiarum Mathematicarum",
volume = "39",
pages = "341--351",
kwds = "la, pert, projection, interpolation"
}
@article{kova:77a,
author = "Z. V. Kovarik",
year = "1977",
title = "Minimal Compatible Solutions of Linear Equations",
journal = "Linear Algebra and Its Applications",
volume = "17",
pages = "95--106",
kwds = "la, linear system, regularization, condition"
}
-kp- -kq- -kr-
@article{krkr:47,
author = "M. G. Krein and M. A. Krasnoselski",
year = "1947",
title = "Fundamental Theorems Concerning the Extension of {Hermitian}
Operators and Some of Their Applications to the Theory
of Orthogonal Polynomials and the Moment Problem",
journal = "Uspekhi Mat. Nauk.",
volume = "2",
note = "In Russian. Cited in \cite{berk:63}.",
kwds = "la, subspace metric, gap, orthogonal polynomial,
symmetric matrix, functional analysis"
}
@article{krkm:48,
author = "M. G. Krein and M. A. Krasnoselski and D. P. Milman ",
year = "1948",
title = "Concerning the Deficiency Numbers of Linear Operators
in {Banach} Space and Some Geometric Questions",
journal = "Sbornik Trudov Inst.\ A. N. Ukr. S. S. R.",
volume = "11",
note = "In Russian. Cited in \cite{berk:63}.",
pages = "",
kwds = "la, subspace metric, gap, functional analysis"
}
@article{krmo:86a,
author = "A. S. Krishnakuma and M. Morf",
year = "1986",
title = "Eigenvalues of a Symmetric Tridiagonal Matrix: A Divide and
Conquer Approach",
journal = "Numerische Mathematik",
volume = "48",
pages = "349--368",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, tridiagonal matrix, symmetric matrix"
}
@article{krog:74,
author = "F. T. Krogh",
year = "1974",
title = "Efficient Implementation of a Variable Projection Algorithm
for Nonlinear Least Squares",
journal = "Communications of the ACM",
volume = "17",
pages = "167--169",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{kron:1866,
author = "L. Kronecker",
year = "1866",
title = "{\"Uber bilineare Formen}",
journal = "{Sitzungberichte der K\"oniglich Preu{\ss}ischen Akademie
der Wissenschaften zu Berlin}",
volume = "",
pages = "597--613",
kwds = "la, geig"
}
@article{kron:1890,
author = "L. Kronecker",
year = "1890",
title = "Algebraische Reduction der Schaaren bilinearer Formen",
journal = "{Sitzungberichte der K\"oniglich Preu{\ss}ischen Akademie
der Wissenschaften zu Berlin}",
volume = "",
pages = "1225--1237",
kwds = "la, Kronecker form, geig"
}
@article{kryl:31,
author = "A. N. Krylov",
year = "1931",
title = "O \v{C}islennom Re\v{s}enii Uravnenija, Kotorym v
techni\v{c}eskih Voprasah Opredeljajutsja \v{c}astoy
malyh kolebani\u{\i} material'nyh",
journal = "Izv. Adad. Nauk SSSR otd. Mat. Estest.",
volume = "",
pages = "491--539",
note = "Cited in \cite{hous:64}.",
kwds = "nla, Krylov sequence, eig"
}
-ks- -kt- -ku-
@article{kubl:61,
author = "V. N. Kublanovskaya",
year = "1961",
title = "On Some Algorithms for the Solution of the Complete
Eigenvalue Problem",
journal = "Zhurnal Vychislitelnoi Matematiki i Matematicheskoi
Fiziki",
volume = "1",
pages = "555--570",
note = "In Russian. Translation in {\it USSR Computational
Mathematics and Mathematical Physics,} {\bf 1} (1962)
637--657",
kwds = "nla, QR algorithm"
}
@article{kufa:64,
author = "V. N. Kublanovskaja and V. N. Faddeeva",
year = "1964",
title = "Computational Methods for the Solution of a Generalized
Eigenvalue Problem",
journal = "Amer. Math. Soc. Transl., Ser. 2",
volume = "40",
pages = "271--290",
kwds = "nla, geig"
}
@article{kubl:68,
author = "V. N. Kublanovskaja",
year = "1968",
title = "An Iteration Process for Obtaining Small Eigenvalues
of a Matrix and the Corresponding Eigenvectors",
journal = "Trudy Mat. Inst. Steklov",
volume = "96",
pages = "113--127",
kwds = "nla, eig"
}
@article{kubl:69,
author = "V. N. Kublanovskaja",
year = "1969",
title = "On an Applicaton of {Newton's} Method to the Determination
of Eigenvalues of $\lambda$-Matrices",
journal = "Dokl. Akad. Nauk SSSR",
volume = "188",
pages = "1240--1241",
note = "Page numbers may refer to AMS translation series.",
kwds = "nla, geig, Newton's method"
}
@article{kubl:70,
author = "V. N. Kublanovskaya",
year = "1970",
title = "On an Approach to the Solution of the Generalized
Latent Value Problem for $\lambda$-Matrices",
journal = "SIAM Journal on Numerical Analysis",
volume = "7",
pages = "532--537",
kwds = "nla, geig, lambda matrix"
}
@inproceedings{kubl:72,
author = "V. N. Kublanovskaya",
year = "1972",
title = "Application of the Orthogonal Transformation to the
Solution of one Extremal Problem",
booktitle = "Information Processing~71",
editor = "",
pages = "1311-1316",
publisher = "North-Holland",
address = "",
kwds = "nlop"
}
@techreport{kubl:81,
author = "V. N. Kublanovskaya",
year = "1981",
title = "AB-Algorithm and Its Modificaton for the Spectral
Problems of Linear Pencils of Matrices",
institution = "Steklov Mathematical Institute",
type = "LOMI Preprint",
number = "E-10-81",
kwds = "nla, geig, AB algorithm, matrix pencil"
}
@article{kumc:72,
author = "D. J. Kuck and Y. Muraoka and S.-C. Chen",
year = "1972",
title = "On the Number of Operations Simultaneously Executable
in {FORTRAN}-Like Programs and Their Resulting Speedup",
journal = "IEEE Transactions on Computers",
volume = "c-21",
pages = "1293--1310",
kwds = "prll, fortran"
}
@techreport{kucz:83,
author = "Jakek Kuczynski",
year = "1983",
title = "Optimality and Sketch of Implementation of the Generalized
Minimal Residual Algorithm for Finding an Eigenpair
of a Large Matrix",
institution = "Department of Mathematics, Link{\"o}ping Univeristy",
type = "Report",
number = "LiTH-Mat-R-83-06",
kwds = "nla, eig, sparse"
}
@article{kumi:86b,
author = "U. W. Kulisch and W. L. Miranker",
year = "1986",
title = "The Arithmetic of the Digital Computer",
journal = "{SIAM} Review",
volume = "28",
pages = "1--40",
note = "Cited in \cite{govl:89}.",
kwds = "na, computer arithmetic, rounding error"
}
@article{kumm:1879,
author = "C. H. Kummell",
year = "1879",
title = "Reduction of Observation Equations Which Contain
More Than One Observed Quantity",
journal = "The Analyst",
volume = "6",
pages = "97--105",
kwds = "regr, eriv"
}
@article{kung:82,
author = "H. T. Kung",
year = "1982",
title = "Why Systolic Architectures?",
journal = "IEEE Computer",
volume = "15",
pages = "37-46",
kwds = "prll, systolic"
}
@inproceedings{karh:81,
author = "S. Y. Kung and K. S. Arun and D. V. Bhaskar Rao and Y. H. Hu",
year = "1981",
title = "A Matrix Data Flow Language/Architecture for
Parallel Matrix Operations Based on Computational Wavefront
Concept",
booktitle = "VLSI Systems and Computation",
editor = "H. T. Kung and B. Sproull and G. Steele",
pages = "235--244",
publisher = "Computer Science Press",
address = "Rockville, Maryland ",
kwds = "nla, prll, data flow, wavefront"
}
@unpublished{kuga:82,
author = "S. Y. Kung and R. J. Gal-Ezer and K. S. Arun",
year = "1982",
title = "Wavefront Array Processor: Architecture, Language and
Application",
note = "``To Appear on Proceedings: Conference on Advanced Research
in VLSI, M.I.T, Cambridge, Massachusetts, January 25-27, 1982.''
Manuscript",
kwds = "nla, prll, wavefront, architecture"
}
@techreport{kume:92,
author = "P. Kunkel and V. Mehrmann",
year = "1992",
title = "Canonical Forms for Linear Differential-Algebraic
Equations with Variable Coefficients",
institution = "{Institut f\"ur Geometrie und Praktische
Mathematik}",
type = "Bericht",
number = "69",
kwds = "la, differential-algebraic equation, canonical form"
}
-kv- -kw- -kx- -ky- -kz-
-la-
@article{laas:59,
author = "P. Laasonen",
year = "1959",
title = "A {Ritz} Method for Simultaneous Determination of Several
Eigenvalues and Eigenvectors of a Big Matrix",
journal = "Annales Academiae Scientiarum Fennicae",
volume = "A I 265",
pages = "3--16",
kwds = "nla, eig, sparse, Rayleigh-Ritz method, subspace iteration,
symmetric matrix"
}
@article{labu:64,
author = "La Budde, C. D.",
year = "1964",
title = "A New Algorithm for Diagonalizing a Real Symmetric
Matrix",
journal = "Mathematics of Computation",
volume = "18",
pages = "118--123",
kwds = "nla, eig, symmetric matrix"
}
@article{labu:64a,
author = "La Budde, C. D.",
year = "1964",
title = "Two New Classes of Algorithms for Finding the Eigenvalues
of Real Symmetric Matrices",
journal = "Journal of the ACM",
volume = "11",
pages = "53--58",
kwds = "nla, eig, symmetric matrix"
}
@article{lash:89,
author = "L.-Y. Lam and K. Shen",
year = "1989",
title = "Methods of Solving Linear Equations in Traditional China",
journal = "Historia Mathematica",
volume = "16",
pages = "107--122",
kwds = "nla, history, linear system, China"
}
@article{lavo:75,
author = "J. Lambiotte and R. G. Voigt",
year = "1975",
title = "The Solution of Tridiagonal Linear Systems on the {CDC-STAR 100}
Computer",
journal = "{ACM} Transactions on Mathematical Software",
volume = "1",
pages = "308--329",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, tridiagonal matrix, vect"
}
@book{lanc:66,
author = "P. Lancaster",
year = "1966",
title = "Lambda-Matrices and Vibrating Systems",
publisher = "Pergamon",
address = "Oxford",
kwds = "book, nla, geig, matrix polynomial, matrix pencil"
}
@article{lanc:70,
author = "P. Lancaster",
year = "1970",
title = "Explicit Solution of Linear Matrix Equations",
journal = "{SIAM} Review",
volume = "12",
pages = "544--566",
note = "Cited in \cite{govl:89}.",
kwds = "nla"
}
@article{lanc:77,
author = "P. Lancaster",
year = "1977",
title = "A Fundemental Theorem on Lambda-Matrices
with Applications---{I}\@. Ordinary Differential
Equations with Constant Coefficients",
journal = "Linear Algebra and Its Applications",
volume = "18",
pages = "189--211",
kwds = "la, lambda matrix, ode"
}
@article{lanc:77a,
author = "P. Lancaster",
year = "1977",
title = "A Fundemental Theorem on Lambda-Matrices with
Applications---{II}\@. Difference Equations with Constant
Coefficients",
journal = "Linear Algebra and Its Applications",
volume = "18",
pages = "213--222",
kwds = "la, lambda matrix, difference equation"
}
@article{laro:77,
author = "P. Lancaster and J. G. Rokne",
year = "1977",
title = "Solutions of Nonlinear Operator Equations",
journal = "SIAM Journal on Mathematical Analysis",
volume = "8",
pages = "448--457",
kwds = "nlop, matrix polynomial"
}
@book{lati:85,
author = "P. Lancaster and M. Tismenetski",
year = "1985",
title = "The Theory of Matrices",
publisher = "Academic Press",
address = "New York",
kwds = "book, la"
}
@article{lanc:50,
author = "C. Lanczos",
year = "1950",
title = "An Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators",
journal = "Journal of Research of the National Bureau of Standards",
volume = "45",
pages = "255--282",
kwds = "nla, eig, Lanczos algorithm, sparse, symmetric matrix"
}
@article{lanc:52,
author = "C. Lanczos",
year = "1952",
title = "Solutions of Linear Equations by Minimized Iterations",
journal = "Journal of Research of the National Bureau of Standards",
volume = "49",
pages = "33--53",
kwds = "nla, conjugate gradients, iter"
}
@article{lanc:58,
author = "C. Lanczos",
year = "1948",
title = "Linear Systems in Self-Adjoint Form",
journal = "American Mathematical Monthly",
volume = "65",
pages = "665--679",
kwds = "la, nla, svd"
}
@article{lang:71,
author = "C. E. Langenhop",
year = "1971",
title = "The Laurent Expansion for a Nearly Singular Matrix",
journal = "Linear Algebra and Its Applications",
volume = "4",
pages = "329--340",
kwds = "la"
}
@article{lang:73,
author = "C. E. Langenhop",
year = "1973",
title = "On the Invertibiliby of a Nearly Singular Matrix",
journal = "Linear Algebra and Its Applications",
volume = "7",
pages = "361--365",
kwds = "la"
}
@book{lapl:1820,
author = "P. S. Laplace",
year = "1820",
title = "Th\'eoria analytique des probabilities (3rd ed.)
premier supplement: Sur l'application du calcul
des probabilit\'es a la philosophie naturelle.
Oeuvres, v.7",
publisher = "Gauthier-Villars",
note = "Supplement published before 1820.",
kwds = "book, probability, Gram-Schmidt algorithm, history"
}
@book{lapl:1886,
author = "P. S. Laplace",
year = "1886",
title = "Th\'eoria Analytique des Probabilities",
publisher = "Oeuvres, 1",
address = "Paris",
edition = "3rd",
kwds = "book, math, probability, history"
}
@article{lpvi:74,
author = "La Porte, M. and J. Vignes",
year = "1974",
title = "Etude statistique des erreurs dans l'arithmetique
des ordinateurs; application au controle des resultats
d'algorithmes numeriques",
journal = "Numerische Mathematik",
volume = "23",
pages = "73--72",
kwds = "na, rounding error, stochastic analysis"
}
@article{lpvi:74a,
author = "La Porte, M. and J. Vignes",
year = "1974",
title = "Methode numerique de detection de la singularite
d'une matrice",
journal = "Numerische Mathematik",
volume = "23",
pages = "73--81",
kwds = "nla, pert, rank determination"
}
@article{lpvi:75,
author = "La Porte, M. and J. Vignes",
year = "1975",
title = "Evalueation de l'incertitude sur la solution
d'un syst\`eme lineaire",
journal = "Numerische Mathematik",
volume = "24",
pages = "39--407",
kwds = "nla, pert, linear system"
}
@article{lasa:78,
author = "J. Larson and A. Sameh",
year = "1978",
title = "Efficient Calculation of the Effects of Roundoff Errors",
journal = "{ACM} Transactions on Mathematical Software",
volume = "4",
pages = "228--236",
note = "Cited in \cite{govl:89}.",
kwds = "na, rounding error"
}
@article{laub:81,
author = "A. Laub",
year = "1981",
title = "Efficient Multivariable Frequency Response Computations",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-26",
pages = "407--408",
note = "Cited in \cite{govl:89}.",
kwds = "nla, control"
}
@article{laub:85,
author = "A. Laub",
year = "1985",
title = "Numerical Linear Algebra Aspects of Control Design Computations",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-30",
pages = "97--108",
note = "Cited in \cite{govl:89}.",
kwds = "nla, control"
}
@article{lhpw:87,
author = "A. J. Laub and M. T. Heath and C. C. Paige and R. C. Ward",
year = "1987",
title = "Computation of System Balancing Transformations and Other
Applications of Simultaneous Diagonalization Algorithms",
journal = "IEEE Transactions on Automatic Control",
volume = "AC-32",
pages = "115--122",
kwds = "control, svd, gsvd"
}
@incollection{laga:88,
author = "A. J. Laub and J. D. Gardiner",
year = "1988",
title = "Hypercube Implementation of Some Parallel Algorithms
in Control",
booktitle = "Advanced Computing Concepts and Techniques in Control
Engineering",
editor = "M. J. Denham and A. J. Laub",
publisher = "Springer-Verlag",
address = "Berlin",
note = "NATO ASI Series, Vol. F47.",
kwds = "control, prll, hypercube"
}
@article{lhkk:79,
author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh",
year = "1979",
title = "Basic Linear Algebra Subprograms for Fortran Usage",
journal = "Application for Computing Machinery Transactions on Mathematical
Software",
volume = "5",
pages = "308-323",
kwds = "nla, software, blas"
}
@book{laha:74,
author = "C. L. Lawson and R. J. Hanson",
year = "1974",
title = "Solving Least Squares Problems",
publisher = "Prentice Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, la, nla, lsq, pert"
}
-lb- -lc- -ld- -le-
@article{lcam:86,
author = "Le Cam, L.",
year = "1986",
title = "The Central Limit Theorem around 1935",
journal = "Statistical Science",
volume = "1",
pages = "78--96",
kwds = "stat, central limit theorem, history"
}
@article{lee:71,
author = "A. Lee",
year = "1971",
title = "Normal Matrix Pencils",
journal = "Periodica Mathematica Hungarica",
volume = "1",
pages = "287--301",
kwds = "la, geig, matrix pencil"
}
@book{lege:1805,
author = "A. M. Legendre",
year = "1805",
title = "Nouvelle m\'ethodes pour la d\'etermination des orbites
des com\`etes",
publisher = "Courcier",
address = "Paris",
note = "Cited in \cite{stig:86}.",
kwds = "book, lsq, history, Legendre"
}
@article{lehm:49,
author = "N. J. Lehmann",
year = "1949",
title = "Calculation of Eigenvalue Bounds in Linear Problems",
journal = "Archiv der Mathematik",
volume = "2",
pages = "139--147",
kwds = "la, eig, pert, symmetric matrix"
}
@article{lehm:63,
author = "N. J. Lehmann",
year = "1963",
title = "{Optimale Eigenwerteinschiessungen}",
journal = "Numerische Mathematik",
volume = "5",
pages = "246--272",
kwds = "la, eig, pert, symmetric matrix"
}
@article{lehm:66,
author = "N. J. Lehmann",
year = "1966",
title = " {Zur Verwendung optimaler Eigenwerteingrenzungen
bei der L\"osung symmetrischer Matrizenaufgaben}",
journal = "Numerische Mathematik",
volume = "8",
pages = "42--55",
kwds = "la, eig, pert, symmetric matrix"
}
@article{lehm:61,
author = "D. H. Lehmer",
year = "1961",
title = "A Machine Method for Solving Polynomial Equations",
journal = "Journal of the ACM",
volume = "8",
pages = "151--162",
kwds = "nlop, polynomial, Lehmer's method"
}
@article{leme:75,
author = "F. Lemeire",
year = "1975",
title = "Bounds for Condition Numbers of Triangular and
Trapezoid Matrices",
journal = "BIT",
volume = "15",
pages = "58--64",
kwds = "nla, pert, condition, triangular matrix"
}
@techreport{lewe:70,
author = "{\"O.} Leringe and P.-\AA. Wedin",
year = "1970",
title = "A Comparison between Different Methods to Compute a
Vector $x$ which Minimizes {$\|Ax-b\|_2$} when
{$Gx=h$}",
institution = "Department of Computer Science, Lund University",
type = "Technical Report",
number = "",
kwds = "nla, lsq, constraints"
}
@article{keve:44,
author = "K. Levenberg",
year = "1944",
title = "A Method for the Solution of Certain Non-Linear
Probelms in Least Squares",
journal = "Quart. Appl. Math.",
volume = "2",
pages = "164--168",
kwds = "nlop, lsq, nllsq, regularization, Levenberg-Marquardt damping"
}
@techreport{letr:83,
author = "R. J. LeVeque and L. N. Trefethen",
year = "1983",
title = "On the Resolvent Condition in the {Kreiss}
Matrix Theorem",
institution = "ICASE",
type = "NASA Contractor Report",
number = "172177",
kwds = "la, Kreiss matrix theorem"
}
@article{levi:65,
author = "A. A. Levin",
year = "1965",
title = "On a Method for the Solution of a Partial Eigenvalue
Problem",
journal = "USSR Computational Mathematics and Mathematical Physics",
volume = "5",
pages = "206--212",
kwds = "nla, eig, sparse"
}
@article{levi:46,
author = "N. Levinson",
year = "1946",
title = "The {Wiener RMS (Root Mean Square)} Error Criterion
in Filter Design and Prediction",
journal = "Journal of Mathematics and Physics",
volume = "25",
pages = "261--278",
kwds = "nla, Toeplitz matrix, Levinson's algorithm, fast algorithm"
}
@article{levy:1881,
author = "L. L\'evy",
year = "1881",
title = "Sur la possibilit\'e du l'\'equilibre \'electrique",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "93",
pages = "706--708",
kwds = "la, pert, diagonal dominance"
}
@techreport{lewi:77,
author = "J. Lewis",
year = "1977",
title = "Algorithms for Sparse Matrix Eigenvalue Problems",
number = "STAN-CS-77-595",
institution = "Department of Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, sparse"
}
-lf- -lg- -lh- -li-
@article{lico:88,
author = "G. Li and T. Coleman",
year = "1988",
title = "A Parallel Triangular Solver for a Distributed-Memory
Multiprocessor",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "9",
pages = "485--502",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, triangular matrix"
}
@article{linp:82,
author = "M. R. Li and B. Nour-Omid and B. N. Parlett",
year = "1982",
title = "A Fast Solver Free of Fill-in for Finite Element Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "19",
pages = "1233--1241",
kwds = "na, nla, finite element, fast algorithm, lud, sparse, pde"
}
@article{lids:50,
author = "V. B. Lidskii",
year = "1950",
title = "The Proper Values of the Sum and
Product of Symmetric Matrices",
journal = "Doklady Akademii Nauk SSSR",
volume = "75",
pages = "769--772",
note = "In Russian. Translation by C.\ Benster available from
the National Translation Center of the Library of Congress.",
kwds = "la, eig, pert, symmetric matrix"
}
@techreport{lizm:91,
author = "C.-C. Lin and E. Zmijewski",
year = "1991",
title = "A Parallel Algorithm for Computing the Eigenvalues
of an Unsymmetric Matrix on an SIMD Mesh of Processors",
institution = "Department of Computer Science, University of
California, Santa Barbara",
type = "Technical Report",
number = "TRCS 91-15",
kwds = "nla, prll, eig, SIMD, matrix sign function, matrix function"
}
@article{lind:47,
author = "D. V. Lindley",
year = "1947",
title = "Regression Lines and the Linear Functional Relationship",
journal = "Supplement to the Journal of the Royal Statistical Society",
volume = "9",
pages = "218-244",
kwds = "stat, regr, eriv, functional model"
}
@article{liwe:84,
author = "P. Lindstr{\"o}m and P.-\AA . Wedin",
year = "1984",
title = "A New Linesearch Algorithm for Unconstrained Nonlinear
Least Squares Problems",
journal = "Math. Programming",
volume = "29",
pages = "268--296",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{ling:74,
author = "R. F. Ling",
year = "1974",
title = "Comparason of Several Algorithms for Computing Means and
Variances",
journal = "Journal of the American Statistical Association",
volume = "69",
pages = "859-866",
kwds = "stat, mean, variance, standard deviation, updating"
}
@book{linn:61,
author = "I. Linnik",
year = "1961",
title = "Method of Least Squares and Principles of the Theory
of Observations",
publisher = "Pergamon Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, stat, lsq"
}
@article{liou:1837,
author = "J. Liouville",
year = "1837",
title = "Second M\'emoir sur le D\'eveloppement des Fonctions en
S\'eries dout les Divers Termes sont Assujettis \`a Satisfaire
\`a une M\^eme \'Equation Differentielle du Second Ordre
Contenant un Parameter Variable.",
journal = "J. Math. Pures Appl.",
volume = "2",
pages = "16-35",
kwds = "math, ode"
}
@article{lirt:79,
author = "R. J. Lipton and D. J. Rose and R. E. Trajan",
year = "1979",
title = "Generalized Nested Dissection",
journal = "SIAM Journal on Numerical Analysis ",
volume = "16",
pages = "346--358",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, nested dissection"
}
@article{litt:35,
author = "D. E. Littlewood",
year = "1935",
title = "On Induced and Compound Matrices",
journal = "Proc. London Math. Soc. (?)",
volume = "",
pages = "370--381",
kwds = "la, Jordan form, compound matrix"
}
@article{liu:86,
author = "J. H. W. Liu",
year = "1986",
title = "On General Row Merging Schemes for Sparse {Givens}
Transformations",
journal = "SIAM Journal on Scientific and Statistical Computing ",
volume = "7",
pages = "1190--1211",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, sparse, plane rotation"
}
@article{liu:90,
author = "J. H. W. Liu",
year = "1990",
title = "The Role of Elimination Trees in Sparse Factorization",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "134--172",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse"
}
-lj- -lk- -ll- -lm- -ln- -lo-
@article{lops:87,
author = "S. Lo and B. Philippe and A. Sameh",
year = "1987",
title = "A Multiprocessor Algorithm for the Symmetric Tridiagonal
Eigenvalue Problem",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "8",
pages = "s155--s165",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, eig, symmetric matrix, tridiagonal matrix"
}
@book{loev:77,
author = "M. Loeve",
year = "1977",
title = "Probability Theory I, II",
publisher = "Springer",
address = "New York",
edition = "4th",
kwds = "book, math, probability"
}
@article{loew:1896,
author = "A. Loewy",
year = "1898",
title = "Sur les formes quadratique d\'efines \`a
ind\'eterminin\'ees conjug\'ees de M Hermite",
journal = "C. R. Acad. Sci. Paris",
volume = "123",
pages = "168-171",
note = "Cited in \cite[p. 79]{macd:46}.",
kwds = "la, symmetric matrix"
}
@article{loiz:69,
author = "G. Loizou",
year = "1969",
title = "Nonnormality and {J}ordan Condition Numbers of Matrices",
journal = "Journal of the {ACM}",
volume = "16",
pages = "580--584",
note = "Cited in \cite{govl:89}.",
kwds = "la, eig, pert, nonormal matrix, condition"
}
@article{loiz:72,
author = "G. Loizou",
year = "1972",
title = "On the Quadratic Convergence of the {J}acobi Method for Normal
Matrices",
journal = "The Computer Journal",
volume = "15",
pages = "274--276",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, normal matrix"
}
@article{long:67,
author = "J. W. Longley",
year = "1967",
title = "An Appraisal of Least Squares Programs for the Electronic
Computer from the Point of View of the User",
journal = "Journal of the American Statistical Association",
volume = "62",
pages = "819-841",
kwds = "stat, nla, rounding error, regr, test matrix"
}
@article{long:81,
author = "J. W. Longley",
year = "1981",
title = "Modified {Gram-Schmidt} Process vs. Classical {Gram-Schmidt}",
journal = "Commun. Statist.-Simula. Computa., B10",
volume = "5",
pages = "517--527",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, regr, Gram-Schmidt algorithm"
}
@book{long:84,
author = "J. W. Longley",
year = "1984",
title = "Least Squares Computations Using Orthogonal Methods",
publisher = "Marcel Dekker, Inc.",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nla, lsq, orthogonalization"
}
@article{lotk:56,
author = "M. Lotkin",
year = "1956",
title = "Characteristic Values of Arbitrary Matrices",
journal = "Quarterly of Applied Mathematics",
volume = "14",
pages = "267--275",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig"
}
@article{lots:83,
author = "P. L{\"o}tstedt",
year = "1983",
title = "Perturbation Bounds for the Linear Least Squares
Problem Subject to Linear Inequality Constraints",
journal = "BIT",
volume = "23",
pages = "500--519",
kwds = "la, lsq, pert, constraints"
}
@article{lots:84,
author = "P. L{\"o}tstedt",
year = "1984",
title = "Solving the Minimal Least Squares Problem Subject to Bounds
on the Variables",
journal = "BIT",
volume = "24",
pages = "206--224",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints"
}
-lp- -lq- -lr- -ls- -lt- -lu-
@article{lu:63,
author = "Lu, Q.-k.",
year = "1963",
title = "The Elliptic Geometry of Extended Space",
journal = "Chinese Mathematics",
volume = "4",
pages = "54--69",
note = "Translation of an article appearing in {\it Acta
mathematica Sinica}, 13 (1963)",
kwds = "la, norm, subspace metric"
}
@article{lu:87,
author = "Lu, T.",
year = "1987",
title = "Solution of the Matrix Equation {$AX - XB = C$}",
journal = "Computing",
volume = "37",
pages = "351-355",
kwds = "nla, Sylvester equation, matrix equation"
}
@article{lube:92,
author = "D. Lubinski and C. P. Benbow",
year = "1992",
title = "Gender Differences in Abilities and Preference
Among the Gifted: Implications for the Math-Science
Pipeline",
journal = "Current Directions in Psychological Science",
volume = "1",
pages = "61--66",
kwds = "math, gender, sex"
}
@inproceedings{lumu:91,
author = "J. C. S. Lui and R. R. Muntz",
year = "1989",
title = "Evaluating Bounds on Staeady State Availability of
Repairable Systems from {Markov} Models",
booktitle = "Numerical Solution of {Markov} Chains",
editor = "W. J. Stewart",
pages = "435--454",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, queue"
}
@phdthesis{luk:78,
author = "F. T. Luk",
year = "1978",
title = "Sparse and Parallel Matrix Computations",
number = "STAN-CS-78-685",
school = "Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, sparse"
}
@article{luk:83,
author = "F. T. Luk",
year = "1983",
title = "Computing the Singular-Value Decomposition
on the {ILLIAC IV}",
journal = "ACM Transactions on Mathematical Software",
volume = "6",
pages = "524--539",
kwds = "nla, prll, svd, illiac"
}
@article{lupa:83,
author = "F. T. Luk and M. Pagano",
year = "1983",
title = "Quadratic Programming with {M}-Matrices",
journal = "Linear Algebra and Its Applications",
volume = "33",
pages = "15--40",
kwds = "nla, quadratic programming, M-matrix"
}
@article{luk:85,
author = "F. T. Luk",
year = "1985",
title = "A Parallel Method for Computing the Generalized
Singular Value Decomposition",
journal = "Journal of Parallel and Distributed Computing",
volume = "2",
pages = "250--260",
kwds = "nla, prll, gsvd"
}
@article{luk:86,
author = "F. T. Luk",
year = "1986",
title = "A Triangular Processor Array for Computing
Singular Values",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "259-274",
kwds = "nla, prll, svd, systolic"
}
@article{luk:86a,
author = "F. T. Luk",
year = "1986",
title = "A Rotation Method for Computing the {QR}-Decomposition",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "452--459",
kwds = "nla, prll, qrd, plane rotation"
}
@article{luqi:87,
author = "F. T. Luk and S. Qiao",
year = "1987",
title = "A Fast but Unstable Orthogonal Triangularization
Technique for {Toeplitz} Matrices",
journal = "Linear Algebra and Its Applications",
volume = "88/89",
pages = "495--506",
kwds = "nla, Toeplitz matrix, fast algorithm, orthogonalization"
}
-lv- -lw- -lx- -ly- -lz-
-ma-
@book{macd:46,
author = "Mac Duffee, C. C.",
year = "1946",
title = "The Theory of Matrices",
publisher = "Chelsea",
address = "New York",
kwds = "book, la"
}
@article{mada:59,
author = "A. Madansky",
year = "1959",
title = "The Fitting of Straight Lines When Both Variables Are Subject to
Error",
journal = "Journal of the American Statistical Association",
volume = "54",
pages = "173--205",
note = "Cited in \cite{govl:89}.",
kwds = "stat, eriv, regr"
}
@article{mark:76,
author = "N. Madsen and G. Roderigue and J. Karush",
year = "1976",
title = "Matrix Multiplication by Diagonals of a Vector Parallel Processor",
journal = "Information Processing Letters",
pages = "41--45",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vect, matrix multiplication"
}
@phdthesis{mahd:81,
author = "N. Mahdavi-Amiri",
year = "1981",
title = "Generally Constrained Nonlinear Least Squares and Generating
Test Problems: Algorithmic Approach",
school = "The John Hopkins University, ",
adress = "Baltimore, MD.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints, test problem"
}
@article{mahi:79,
author = "K. N. Mahindar",
year = "1979",
title = "Linear Combinations of {H}ermitian and Real Symmetric Matrices",
journal = "Linear Algebra and its Applications",
volume = "25",
pages = "95--105",
note = "Cited in \cite{govl:89}.",
kwds = "la, symmetric matrix"
}
@article{makh:75,
author = "J. Makhoul",
year = "1975",
title = "Linear Prediction: A Tutorial Review",
journal = "Proceedings of the {IEEE}",
volume = "63(4)",
pages = "561--580",
note = "Cited in \cite{govl:89}.",
kwds = "linear prediction, time series"
}
@article{mapa:74,
author = "M. A. Malcolm and J. Palmer",
year = "1974",
title = "A Fast Method For Solving a Class of Tridiagonal Systems of Linear
Equations",
journal = "Communications of the {ACM}",
volume = "17",
pages = "14--17",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, tridiagonal matrix, fast algorithm"
}
@article{mall:73,
author = "C. L. Mallows",
year = "1973",
title = "Some Comments on {$C_P$}",
journal = "Technometrics",
volume = "15",
pages = "661--675",
kwds = "stat, regr, diagnostic"
}
@phdthesis{mann:85,
author = "P. Manneback",
year = "1985",
title = "On Some Numerical Methods for Solving Large Sparse Linear
Least Squares Problems",
school = "Facult\'es Universitaires Notre-Dame de la Paix",
adress = "Namur, Belgium.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{mamt:85,
author = "P. Manneback and C. Murigande and P. L. Toint",
year = "1985",
title = "A Modification of an Algorithm by {Golub} and {Plemmons} for Large
Linear Least Squares in the Context of {Doppler} Positioning",
journal = "IMA J. Numer. Anal.",
volume = "5",
pages = "221--234",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse"
}
@article{mant:77,
author = "T. A. Manteuffel",
year = "1977",
title = "The Tchebychev Iteration for Nonsymmetric Matrices",
journal = "Numerische Mathematik",
volume = "28",
pages = "307--327",
kwds = "nla, linear system, sparse, nonsymmetric matrix"
}
@article{mant:78,
author = "T. A. Manteuffel",
year = "1978",
title = "Adaptive Procedure for Estimation of Parameter for the
nonsymmetric Tchebychev Iteration",
journal = "Numerische Mathematik",
volume = "31",
pages = "183--208",
kwds = "nla, linear system, sparse, nonsymmetric matrix"
}
@inproceedings{mant:79,
author = "T. A. Manteuffel",
year = "1979",
title = "Shifted Incomplete {C}holesky Factorization",
booktitle = "Sparse Matrix Proceedings 1978",
editor = "I. S. Duff and G. W. Stewart",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Cholesky decomposition, incomplete factorization"
}
@article{mant:80,
author = "T. A. Manteuffel",
year = "1980",
title = "An Incomplete Factorization Technique for Positive Definite
Linear System",
journal = "Mathematics of Computation",
volume = "34",
pages = "473--497",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, preconditioning, incomplete factorization"
}
@article{mant:81,
author = "T. A. Manteuffel",
year = "1981",
title = "An Interval Analysis Approach to Rank Determination
in Linear Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistal Computing",
volume = "2",
pages = "335--348",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "math, nla, lsq, rank determination, weights, interval arithmetic"
}
@article{maoc:91,
author = "E. Marchi and J. A. Oviedo and J. E. Cohen",
year = "1991",
title = "Pertrubation Theory of a Nonlinear Game of
von {Neuman}",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "592--596",
kwds = "nla, nlop, eig, pert, game theory"
}
@book{marc:60,
author = "M. Marcus",
year = "1960",
title = "Basic Theorems in Matrix Theory",
series = "Applied Mathematics Series \#57",
publisher = "National Bureau of Standards",
address = "Washington, D.C.",
kwds = "book, la"
}
@book{mami:64,
author = "M. Marcus and H. Minc",
year = "1964",
title = "A Survey of Matrix Theory and Matrix Inequalities",
publisher = "Allyn and Bacon",
address = "Boston",
kwds = "book, la, eig, pert, inequalities"
}
@techreport{masz:91,
author = "I. Marek and D. B. Szyld",
year = "1991",
title = "Iterative Aggregation with Inexact Correction",
institution = "Department of Mathematics, Temple University",
type = "Technical Report",
number = "91--52",
kwds = "nla, eig, Markov chain, aggregation, linear system"
}
@article{manp:85,
author = "T. L. Markham and M. Neumann and R. J. Plemmons",
year = "1985",
title = "Convergence of a Direct-iterative Method for Large-scale
Least-squares Problems",
journal = "Linear Algebra and Its Applications",
volume = "69",
pages = "155--167",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, iter, preconditioning"
}
@book{mark:12,
author = "A. A. Markoff",
year = "1912",
title = "Wahrscheinlichheitsrechnung",
publisher = "Leipzig",
address = "Berlin",
edition = "2nd",
kwds = "book, probability, lsq, Gauss-Markov theorem"
}
@article{mark:57,
author = "H. M. Markowitz",
year = "1957",
title = "The Elimination Form of the Inverse and its Application to
Linear Programming",
journal = "Management Science",
volume = "3",
pages = "255--269",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear programming, inverse matrix"
}
@article{marq:63,
author = "D. W. Marquardt",
year = "1963",
title = "An Algorithm for Least-Squares Estimation of
Nonlinear Parameters",
journal = "Journal of the Society for Industrial and Applied Mathematics",
volume = "11",
pages = "431--441",
kwds = "nlop, lsq, nllsq, Levenberg-Marquardt damping, regularization"
}
@article{marq:70,
author = "D. W. Marquardt",
year = "1970",
title = "Generalized Inverses, Ridge Regression, Biased Linear Estimation,
and Nonlinear Regression",
journal = "Technometrics",
volume = "12",
pages = "591-613",
kwds = "stat, regr, nlop, ginv, ridge regression,"
}
@article{masn:75,
author = "D. W. Marquardt and R. D. Snee",
year = "1975",
title = "Ridge Regression in Practice",
journal = "The American Statistician",
volume = "29",
pages = "3--20",
kwds = "stat, regr, ridge regression"
}
@article{marq:80,
author = "D. W. Marquardt",
year = "1980",
title = "Comment on {Smith} and {Campbell} (1980)",
journal = "Journal of the American Statistical Association",
volume = "75",
pages = "87-91",
kwds = "stat, regr, eriv, ridge regression, centering"
}
@techreport{maol:67,
author = "A. W. Marshall and I. Olkin",
year = "1967",
title = "Scaling of Matrices to Achieve Specified Column
and Row Sums",
institution = "Boeing Scientific Research Laboratories",
type = "Mathematical Note",
number = "526",
kwds = "la, Sinkhorn's theorem, stochastic matrix"
}
@article{mawi:65,
author = "R. S. Martin and J. H. Wilkinson",
year = "1965",
title = "Symmetric Decomposition of Positive Definite Band
Matrices",
journal = "Numerische Mathematik",
volume = "7",
pages = "335--361",
note = "Also in \cite[pp.50--56]{wire:71}.",
kwds = "nla, lud, band matrix, symmetric matrix, software"
}
@article{mapw:65,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
year = "1965",
title = "Symmetric Decomposition of a Positive Definite Matrix",
journal = "Numerische Mathematik",
volume = "7",
pages = "363--383",
note = "Also in \cite[pp.9--30]{wire:71}.",
kwds = "nla, Cholesky decomposition, software"
}
@article{mapw:66,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
year = "1966",
title = "Iterative Refinement of the Solution of a Positive
Definite System of Equations",
journal = "Numerische Mathematik",
volume = "8",
pages = "203--216",
note = "Also in \cite[pp.31--49]{wire:71}.",
kwds = "nla, linear system, iterative refinement,
positive definite matrix, software"
}
@article{mawi:67,
author = "R. S. Martin and J. H. Wilkinson",
year = "1967",
title = "Solution of Symmetric and Unsymmetric Band Equations
and the Calculation of Eigenvectors of Band Matrices",
journal = "Numerische Mathematik",
volume = "9",
pages = "279--301",
note = "Also in \cite[pp.70--92]{wire:71}.",
kwds = "nla, linear system, eig, band matrix, software"
}
@article{marw:68,
author = "R. S. Martin and C. Reinsch and J. H. Wilkinson",
year = "1968",
title = "Householder Tridiagonalization of a Real Symmetric Matrix",
journal = "Numerische Mathematik",
volume = "11",
pages = "181--195",
note = "Also in \cite[pp.212--226]{wire:71}.",
kwds = "nla, eig, Householder transformation, symmetric matrix,
tridiagonal matrix, software"
}
@article{mawi:68,
author = "R. S. Martin and J. H. Wilkinson",
year = "1968",
title = "Similarity Reduction of a General Matrix to
{Hessenberg} Form",
journal = "Numerische Mathematik",
volume = "12",
pages = "369--378",
note = "Also in \cite[pp.339--358]{wire:71}.",
kwds = "nla, eig, nonsymmetric matrix, Hessenberg matrix, software"
}
@article{mawi:68a,
author = "R. S. Martin and J. H. Wilkinson",
year = "1968",
title = "The Modified {LR}~Algorithm for Complex {Hessenberg}
Matrices",
journal = "Numerische Mathematik",
volume = "12",
pages = "369--376",
note = "Also in \cite[pp.396--403]{wire:71}.",
kwds = "nla, eig, LR algorithm, complex matrix,
Hessenberg matrix, software"
}
@article{mawi:68b,
author = "R. S. Martin and J. H. Wilkinson",
year = "1968",
title = "Reduction of the Symmetric Eigenproblem
{$Ax=\lambda Bx$} and Related Problems to Standard Form",
journal = "Numerische Mathematik",
volume = "11",
pages = "99--110",
note = "Also in \cite[pp.303--314]{wire:71}.",
kwds = "nla, geig, symmetric matrix, software"
}
@article{mawi:68c,
author = "R. S. Martin and J. H. Wilkinson",
year = "1968",
title = "Reduction of the Symmetric Eigenproblem {$Ax = \lambda Bx$} and
Related Problems to Standard Form",
journal = "Numerische Mathematik",
volume = "11",
pages = "99--110",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig"
}
@article{mapw:70,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
year = "1970",
title = "The {QR}~Algorithm for real {Hessenberg} matrices",
journal = "Numerische Mathematik",
volume = "14",
pages = "219--231",
note = "Also in \cite[pp.359--371]{wire:71}.",
kwds = "nla, eig, QR algorithm, Hessenberg matrix, software"
}
@article{masc:58,
author = "J. L. Massera and J. J. Sch{\"a}ffer",
year = "1958",
title = "Linear Differential Equations and Functional Analysis {I}",
journal = "Annals of Math.",
volume = "67",
pages = "517--573",
note = "Cited in \cite{berk:63}.",
kwds = "la, norm, subspace metric, functional analysis"
}
@article{math:92,
author = "R. Mathias",
year = "1992",
title = "Matrices with Positive Definite Hermitian Part:
Inequalities and Linear Systems",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "640--654",
kwds = "nla, positive definite matrix, linear system"
}
@phdthesis{mats:91,
author = "P. Matstoms",
year = "1991",
title = "The Multifrontal Solution of Sparse Linear Least Squares Problems",
school = "Link{\"o}ping University",
institution = "Department of Mathematics",
adress = "Link{\"o}ping, Sweden",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, sparse, qrd"
}
@inproceedings{mame:91,
author = "R. B. Mattingly and C. D. Meyer",
year = "1991",
title = "Computing the Stationary Distribution Vector of
an Irreducible {Markov} Chain on a Shared-Memory
Multiprocessor",
booktitle = "Numerical Solution of {Markov} Chains",
editor = "W. J. Stewart",
pages = "491--510",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, Schur complement, prll"
}
-mb- -mc-
@article{mcss:84,
author = "D. F. McAllister and G. W. Stewart and W. J. Stewart",
year = "1984",
title = "On a {Rayleigh--Ritz} Refinement Technique
for Nearly Uncoupled Stochastic Matrices",
journal = "Linear Algebra and Its Applications",
volume = "60",
pages = "1--25",
kwds = "nla, Markov chain, nearly uncoupled system, Rayleigh-Ritz method, aggregation"
}
@article{mcvv:87,
author = "O. A. McBryan and van de Velde, Eric F.",
year = "1987",
title = "Hypercube Algorithms and Implementations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "227--287",
kwds = "prll, hypercube"
}
@article{mcst:73,
author = "C. McCarthy and G. Strang",
year = "1973",
title = "Optimal Conditioning of Matrices",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "10",
pages = "370--388",
note = "Cited in \cite{govl:89}.",
kwds = "nla, condition, scaling"
}
@article{mcco:72,
author = "S. F. McCormick",
year = "1972",
title = "A General Approach to One-Step Iterative Methods with
Application to Eigenvalue Problems",
journal = "Journal of Computer and System Sciences",
volume = "6",
pages = "354--372",
kwds = "nla, eig, sparse"
}
@unpublished{mcno:??,
author = "S. F. McCormick and T. Noe",
year = "19??",
title = "Simultaneous Iteration for the Matrix Eigenvalue Problem",
note = "Manuscript. Department of Mathematics, Colorado State
University",
kwds = "nla, eig, subspace iteration, sparse"
}
@article{mcro:75,
author = "S. F. McCormick and G. H. Rodrigue",
year = "1975",
title = "A Uniform Approach to Gradient Methods for Linear
Operator Equations",
journal = "Journal of Mathematical Analysis and Applications",
volume = "49",
pages = "275--285",
kwds = "nla, gradient methods, linear system, conjugate gradients"
}
@book{mcco:83,
author = "G. P. McCormic",
year = "1983",
title = "Nonlinear Programming",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, nlop"
}
@unpublished{mcea:90,
author = "R. McEachin",
year = "1990",
title = "A Sharp Estimate in an Operator Inequality",
note = "Manuscript, Department of Mathematical Sciences,
Indiana University, Fort Wayne, IN. To appear
in the {\it Proceedings of the AMS\/}",
kwds = "la, pert, eig"
}
@unpublished{mcea:90a,
author = "R. McEachin",
year = "1990",
title = "Closing the Gap in a Subspace Perturbation Bound",
note = "Manuscript, Department of Mathematical Sciences,
Indiana University, Fort Wayne, IN.
Submitted to {\it Linear Algebra and Its Applications\/}",
kwds = "la, pert, eig"
}
@article{mipr:87,
author = "A. McIntosh and A. Pryde",
year = "1987",
title = "A Functional Calculus for Several Commuting Operators",
journal = "Indiana University Mathematics Journal",
volume = "36",
pages = "421--439",
kwds = "la, commuting matrices, Clifford algebra"
}
@article{mipr:88,
author = "A. McIntosh and A. Pryde and W. Ricker",
year = "1987",
title = "Comparison of Joint Spectra for Certain Classes of
Commuting Matrices",
journal = "Studia Mathematica",
volume = "88",
pages = "23--36",
kwds = "la, commuting matrices"
}
@article{mkee:62,
author = "W. M. McKeeman",
year = "1962",
title = "Crout with Equilibration and Iteration",
journal = "Communications of the {ACM}",
volume = "5",
pages = "553--555",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, scaling, iterative refinement"
}
@article{mcco:69,
author = "A. C. McKellar and E. G. Coffman",
year = "1969",
title = "Organizing Matrices and Matrix Operations for Paged
Memory Systems",
journal = "Communications of the Association for Computing
Machinery",
volume = "13",
pages = "153--165",
kwds = "nla, memory hierarchy"
}
@inproceedings{mcmi:81,
author = "J. McKenna and D. Mitra",
year = "1981",
title = "Integral Representations and Asymptotic Expansions
for Closed {Markovian} Queueing Networks: Normal
Usage",
booktitle = "Performance '81",
editor = "F. J. Kylstra",
pages = "67--83",
publisher = "North-Holland",
address = "Amsterdam",
kwds = "nla, queue, Markov chain"
}
-md- -me-
@article{meva:68,
author = "H. I. Medley and R. S. Varga",
year = "1968",
title = "On Smallest Isolated Gerschgorin Disks for Eigenvalues.~{III}",
journal = "Numerische Mathematik",
volume = "11",
pages = "361--369",
kwds = "la, eig, Gerschgorin's theorem"
}
@book{mehr:91,
author = "V. L. Mehrmann",
year = "1991",
title = "The Autonomous Linear Quadratic Control Problem",
publisher = "Springer",
address = "New York",
series = "Lecture Notes in Control and Information Sciences, 163",
kwds = "book, la, nla, control"
}
@techreport{mehr:91a,
author = "V. L. Mehrmann",
year = "1991",
title = "Divide and Conquer Methods for Block Tridiagonal Systems",
institution = "Institut {f\"ur} Geometrie and Praktische Mathematik,
RWTH Aachen",
type = "Bericht",
number = "68",
kwds = "nla, tridiagonal matrix, prll, domain decomposition"
}
@article{mevv:77,
author = "J. A. Meijerink and van der Vorst, H. A.",
year = "1977",
title = "An Iterative Solution Method for Linear Systems
of Which the Coefficient Matrix is a Symmetric
{$M$}-Matrix",
journal = "Mathematics of Computation",
volume = "31",
pages = "148--162",
kwds ="nla, linear system, iter, M-matrix, symmetric matrix"
}
@article{mein:83,
author = "J. Meinguet",
year = "1983",
title = "Refined Error Analysis of {Cholesky} Factorization",
journal = "SIAM Journal on Numerical Analysis",
volume = "20",
pages = "1243--1250",
kwds = "nla, rounding error, lud, Cholesky decomposition"
}
@techreport{meis:80,
author = "P. Meissl",
year = "1980",
title = "A Priori Prediction of Roundoff Error Accumulation in the
Solution of a Super-Large Geodetic Normal Equation System",
institution = "National Oceanic and Atmospheric Administration",
type = "Professional Paper",
number = "12",
kwds = "nla, geodesy, lsq, rounding error, normal equations"
}
@article{melh:87,
author = "R. Melhem",
year = "1987",
title = "Toward efficient Implementation of Preconditioned Conjugate
Gradient Methods on Vector Supercomputers",
journal = "International Journal of Supercomputing Applications",
volume = "1",
pages = "70--98",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning, vect"
}
@article{merr:1877,
author = "M. Merriman",
year = "1977",
title = "A List of Writings Relating to the Method of Least
Squares with Historical and Critical Notes",
journal = "Transactions of the Conneticticut Academy of Arts
and Sciences",
volume = "4",
pages = "151--231",
kwds = "stat, lsq, regr, history",
annote = "Reproduced [in typscript] by the Statistical Engineering
Laboratory of the National Bureau of Standards for
the convenience of its staff. March 1957l. W-57-3"
}
@book{merr:1884,
author = "M. Merriman",
year = "1884",
title = "A Text-Book on the Method of Least Squares",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr, lsq"
}
@article{merr:85,
author = "M. L. Merriam",
year = "1985",
title = "On the Factorization of Block Tridiagonals With Storage
Constraints",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "6",
pages = "182--192",
note = "Cited in \cite{govl:89}.",
kwds = "nla, block algorithm, block tridiagonal matrix, lud"
}
@article{meur:84,
author = "G. Meurant",
year = "1984",
title = "The Block Preconditioned Conjugate Gradient Method on Vector
Computers",
journal = "{BIT}",
volume = "24",
pages = "623--633",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, preconditioning, block algorithm,
vect"
}
@article{meur:89,
author = "G. Meurant",
year = "1989",
title = "Domain Decomposition Methods for Partial Differential Equations on
Parallel Computers",
journal = "International Journal of Supercomputing Applications",
note = "To appear",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pde, domain decomposition, prll"
}
@article{meye:80,
author = "C. D. Meyer",
year = "1980",
title = "The Condition of a {Markov} Chain and Perturbations Bounds
for the Limiting Probabilities",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "1",
pages = "273--283",
kwds = "la, pert, eig, Markov chain, condition"
}
@article{mest:88,
author = "C. Meyer and G. W. Stewart",
year = "1988",
title = "Derivatives and Perturbations of Eigenvectors",
journal = "SIAM Journal on Numerical Analysis",
volume = "25",
pages = "679-691",
kwds = "math, la, pert, eig, matrix derivative, condition"
}
@article{meye:89,
author = "C. D. Meyer",
year = "1989",
title = "Stochastic Complementation, Uncoupling {Markov}
Chains, and the Theory of Nearly Reducible Systems",
journal = "SIAM Review",
volume = "31",
pages = "240--272",
kwds = "nla, Schur complement, Markov chain, nearly uncoupled system"
}
@article{meye:89a,
author = "C. D. Meyer",
year = "1989",
title = "Uncoupling the {Perron} Eigenvector Problem",
journal = "Linear Algebra and Its Applications",
volume = "114/115",
pages = "69--94",
kwds = "la, nonnegative matrix, Schur complement, Markov chain"
}
@techreport{meye:91,
author = "C. D. Meyer",
year = "1991",
title = "Sensitivity of {Markov} Chains",
institution = "Mathematics Department, North Carolina State University",
type = "Technical Report",
number = "1271992709",
kwds = "la, pert, Markov chain"
}
@article{mesp:72,
author = "R. Meyer-Spasche",
year = "1972",
title = "A Method of Solving the Stability Problem for Complex
Matrices",
journal = "Numerische Mathematik",
volume = "20",
pages = "364--371",
kwds = "nla, eig, stability"
}
-mf- -mg- -mh- -mi-
@article{mill:89,
author = "A. J. Miller",
year = "1989",
title = "Updating Means and Variances",
journal = "Journal of Computational Physics",
volume = "85",
pages = "500--501",
kwds = "stat, mean, variance, correlation, update, software"
}
@article{misp:78,
author = "W. Miller and D. Spooner",
year = "1978",
title = "Software for Roundoff Analysis, {II}",
journal = "{ACM} Transactions on Mathematical Software",
volume = "4",
pages = "369--390",
note = "Cited in \cite{govl:89}.",
kwds = "cs, rounding error, software"
}
@article{mill:75,
author = "W. Miller",
year = "1975",
title = "Computational Complexity and Numerical Stability",
journal = "SIAM Journal on Computing",
volume = "4",
pages = "97--107",
kwds = "na, rounding error, complexity"
}
@book{miwr:80,
author = "W. Miller and C. Wrathall",
year = "1980",
title = "Software for Roundoff Analysis of Matrix Algorithms",
publisher = "Academic Press",
address = "New York",
kwds = "book, nla, rounding error, software"
}
@article{mipa:82,
author = "G. Miminis and C. C. Paige",
year = "1982",
title = "An Algorithm for Pole Assignment of Time Invariant Linear Systems",
journal = "International Journal of Control",
volume = "35",
pages = "341--354",
note = "Cited in \cite{govl:89}.",
kwds = "nla, control, pole assignment"
}
@article{mipa:91,
author = "G. S. Miminis and C. C. Paige",
year = "1991",
title = "Implicit Shifting in the {QR}~and Related Algorithms",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "385--400",
kwds = "nla, QR algorithm, eig"
}
@book{mink:1896,
author = "H. Minkowski",
year = "1896",
title = "{Geometrie der Zahlen. I\@.}",
publisher = "B. G. Teubner",
address = "Leipzig",
note = "Cited in \cite{bebe:71}.",
kwds = "book, Minkowski inequality"
}
@incollection{mink:11,
author = "H. Minkowski",
year = "1911, posthumous",
title = "Theorie der {Konvexen} {K\"orper},
insbesondere {Begr\"undung} ihres {Oberfl\"achenbegriffs}",
booktitle = "Minkowski Abhandlung",
publisher = "Teubner Verlag",
editor = "David Hilbert",
kwds = "math, convexity, norm"
}
@article{mirs:59,
author = "L. Mirsky",
year = "1959",
title = "Proofs of Two Theorems on Doubly Stochastic Matrices",
journal = "Proceedings of the American Mathematical Society",
volume = "9",
pages = "371--374",
kwds = "la, doubly stochastic matrix"
}
@article{mirs:60,
author = "L. Mirsky",
year = "1960",
title = "Symmetric Gauge Functions and Unitarily Invariant Norms",
journal = "Quarterly Journal of Mathematics",
volume = "11",
pages = "50-59",
kwds = "math, la, norm, svd, Schmidt-Mirsky theorem"
}
@article{mirs:63,
author = "L. Mirsky",
year = "1963",
title = "Results and Problems in the Theory of Doubly Stochastic
Matrices",
journal = " {Zeitschrift f\"ur Wahrscheinlichkeitstheorie und
verwandte Gebiete}",
volume = "1",
pages = "319--334",
kwds = "la, Markov chain, doubly stochastic matrix"
}
@article{mimi:90,
author = "D. Mitra and I. Mitrani",
year = "1990",
title = "Analysis of a Kanban Discipline for Cell Coordination
in Production Lines, {II}: Stochastic Demands",
journal = "Operations Research",
volume = "39",
pages = "807--823",
kwds = "queue, Markov chain"
}
@book{mitr:70,
author = "D. S. Mitrinovi{\'c}",
year = "1970",
title = "Analytic Inequalities",
publisher = "Springer",
address = "New York",
kwds = "book, inequalities"
}
@inproceedings{mits:87,
author = "D. Mitra and P. Tsoucas",
year = "1987",
title = "Convergence of Relaxations for Numerical Solutions
of Stochastic Problems",
booktitle = "Second International Workshop on Applied
Mathematics and Performance/Reliability Models
of Computer/Communication Sytems",
editor = "G. Iazeolla and P.-J. Courtois and O. J. Boxma",
pages = "119--133",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, queue, iter, relaxation"
}
-mj- -mk- -ml- -mm- -mn- -mo-
@article{mocl:84,
author = "J. J. Modi and M. R. B. Clarke",
year = "1984",
title = "An Alternative {Givens} Ordering",
journal = "Numerische Mathematik",
volume = "43",
pages = "83--90",
kwds = "nla, qrd, plane rotation"
}
@article{mopr:85,
author = "J. J. Modi and J. D. Pryce",
year = "1985",
title = "Efficient Implementation of {J}acobi's Diagonalization Method
on the {DAP}",
journal = "Numerische Mathematik",
volume = "46",
pages = "443--454",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, prll"
}
@book{modi:88,
author = "J. J. Modi",
year = "1988",
title = "Parallel Algorithms and Matrix Computation",
publisher = "Oxford University Press",
address = "Oxford",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, prll"
}
@article{mole:67,
author = "C. B. Moler",
year = "1967",
title = "Iterative Refinement in Floating Point",
journal = "Journal of the ACM",
volume = "14",
pages = "316--321",
kwds = "nla, lud, iterative refinement"
}
@article{mole:72,
author = "C. B. Moler",
year = "1972",
title = "Matrix Computations with {Fortran} and Paging",
journal = "Communications of the ACM",
volume = "15",
pages = "268-270",
kwds = "nla, memory hierarchy, fortran"
}
@article{most:73,
author = "C. B. Moler and G. W. Stewart",
year = "1973",
title = "An Algorithm for Generalized Matrix Eigenvalue Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "241--256",
kwds = "nla, geig, QZ algorithm"
}
@article{most:78,
author = "C. B. Moler and G. W. Stewart",
year = "1978",
title = "On the Householder-Fox Algorithm for
Decomposing a Projection",
journal = "Journal of Computational Physics",
volume = "28",
pages = "82--91",
kwds = "nla, projection, rounding error, lud"
}
@article{movl:78,
author = "C. B. Moler and Van Loan, C. F.",
year = "1978",
title = "Nineteen Dubious Ways to Compute the Matrix Exponential",
journal = "SIAM Review",
volume = "20",
pages = "801--836",
kwds = "nla, matrix exponential, eig, matrix function"
}
@techreport{mole:80,
author = "C. B. Moler",
year = "1980",
title = "{MATLAB}\,---\,An Interactive Matrix Laboratory",
institution = "Department of Mathematics and Statistics,
University of New Mexico",
type = "Technical Report",
number = "369",
kwds = "nla, software"
}
@techreport{mole:82,
author = "C. B. Moler",
year = "1982",
title = "{MATLAB} Users' Guide",
institution = "Department of Computer Science,
University of New Mexico",
number = "CS81-1 (Revised)",
kwds = "nla, software"
}
@article{momo:83,
author = "C. B. Moler and D. Morrison",
year = "1983",
title = "Singular Value Analysis of Cryptograms",
journal = "American Mathematical Monthly",
volume = "90",
pages = "78--87",
note = "Cited in \cite{govl:89}.",
kwds = "nla, svd, application"
}
@incollection{mole:86,
author = "C. B. Moler",
year = "1986",
title = "Matrix Computations on Distributed Memory Multiprocessors",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll"
}
@book{molb:87,
author = "C. Moler and J. Little and S. Bangert",
year = "1987",
title = "Pro-Matlab User's Guide",
publisher = "The Math Works",
address = "Shereborn, MA",
kwds = "book, nla, software"
}
@incollection{moli:77,
author = "L. Molinari",
year = "1977",
title = "{Gram-Schmidt'sches Orthogonalisierungsverfahren}",
booktitle = "{Numerische Prozeduren aus Nachlass und Lehre
von Prof. Heinz Rutishauser}",
editor = "W. Gander, L. Molinari and H. Svecov\'a",
pages = "77--93",
publisher = "Birkh{\"a}user",
address = "Stuttgart",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Gram-Schmidt algorithm"
}
@article{mosp:81,
author = "C. J. Monlezun and F. M. Speed",
year = "1981",
title = "Recovering Sums of Squares between Full and Reduced Linear Models",
journal = "Communications in Statistics",
volume = "10",
pages = "875-882",
note = "Part A",
kwds = "stat, regr"
}
@article{mola:82,
author = "R. Montoye and D. Laurie",
year = "1982",
title = "A Practical Algorithm for the Solution of Triangular Systems on a
Parallel Processing System",
journal = "{IEEE} Transactions on ",
volume = "C-31",
pages = "1076--1082",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, triangular matrix"
}
@techreport{moon:79,
author = "Y.-S. Moon",
year = "1979",
title = "On the Numerical Solution of the Definite Generalized
Eigenvalue Problem",
institution = "Department of Computer Science, University of
Toronto",
type = "Technical Report",
number = "135/79",
kwds = "nla, geig, symmetric matrix"
}
@phdthesis{moon:90,
author = "M. Moonen",
year = "1990",
title = "{Jacobi}-Type Updating Algorithms for Signal Processing,
Systems Identification and Control",
school = "Katholieke Universiteit Leuven",
kwds = "nla, Jacobi-like, updating, svd, qrd, signal processing,
control"
}
@inproceedings{movv:91,
author = "M. Moonen and Van Dooren, P. and J. Vandewalle",
year = "1991",
title = "Combined {Jacobi}-Type Algorithms in Signal Processing",
booktitle = "SVD and Signal Processing, {II}",
editor = "R. J. Vaccaro",
pages = "177--188",
publisher = "Elsevier Science Publishers",
address = "Amsterdam",
kwds = "nla, svd, updating, Jacobi-like"
}
@article{movv:91a,
author = "M. Moonen and Van Dooren, P. and J. Vandewalle",
year = "1991",
title = "A Note on ``Efficient Numerically Stabilized Rank-One
Eigenstructure Updating",
journal = "IEEE Transactions on Signal Processing",
volume = "39",
pages = "1911--1913",
note = "Reply by DeGroat, pp.~1913--1914.",
kwds = "nla, eig, orthogonalization, updating, scaling"
}
@article{mova:91,
author = "M. Moonen and J. Vandewalle",
year = "1991",
title = "A Square Root Covariance Algorithm for Constrained
Recursive Least Squares Estimation",
journal = "Journal of VLSI Signal Processing",
volume = "3",
pages = "163--172",
kwds = "nla, lsq, updating, constraints"
}
@article{moor:20,
author = "E. H. Moore",
year = "1920",
title = "On the Reciprocal of the General Algebraic Matrix",
journal = "Bulletin of the American Mathematical Society",
volume = "26",
pages = "394-395",
note = "Abstract.",
kwds = "la, ginv"
}
@book{moor:35,
author = "E. H. Moore",
year = "1935",
title = "General Analysis",
series = "Memoirs of the American Philosophical Society, I",
publisher = "American Philosophical Society",
address = "Philadelphia, Pennsylvania",
kwds = "book, la, ginv"
}
@article{mora:71,
author = "P. A. P. Moran",
year = "1971",
title = "Estimating Structural and Functional Relationships",
journal = "Journal of Multivariate Analysis",
volume = "1",
pages = "232-255",
kwds = "stat, regr, eriv, functional model, structural model"
}
@inproceedings{more:78,
author = "J. J. Mor\'e",
year = "1978",
title = "The {Levenberg-Marquardt} Algorithm: Implementation and Theory",
booktitle = "G.A. Watson",
pages = "105--116",
publisher = "Springer Verlag",
series = "Lecture Notes in Mathematics 630",
address = "Berlin",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Levenberg-Marquardt damping"
}
@techreport{mogh:80,
author = "J. J. Mor\'e and B. S. Garbow and K. E. Hillstrom",
year = "1980",
title = "Users' Guide for {MINPACK-1}",
institution = "Applied Math. Div., Argonne National Laboratory.",
type = "Technical Report",
number = "ANL-80-74",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, software"
}
@inproceedings{more:83,
author = "J. J. Mor\'e",
year = "1983",
title = "Recent Developments in Algorithms and Software for
Trust Region-methods",
booktitle = "Mathematical Programming. The State of the Art,
Proceedings Bonn 1982",
editor = "",
pages = "",
publisher = "Springer Verlag",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, software"
}
@article{mcdd:91,
author = "J. P. Morgan and N. R. Chaganty and R. C. Dahiya and
M. J. Doviak",
year = "1991",
title = "Let's Make a Deal: The Player's Dilemma",
journal = "The American Statistician",
volume = "45",
pages = "284--287",
note = "With comment by R. G. Seymann (pp.~287--288)
and rejoinder (p.~289).",
kwds = "stat, Monte Hall paradox"
}
@article{moti:77,
author = "B. J. T. Morgan and D. M. Titterington",
year = "1977",
title = "A Comparison of Iterative Methods for Obtaining Maximum
Likelihood Estimates in Contingency Tables with a
Missing Diagonal",
journal = "Biometrika",
volume = "64",
pages = "265--269",
kwds = "stat, contingency table, categorical data"
}
@book{motu:77,
author = "F. Mosteller and J. W. Tukey",
year = "1977",
title = "Data Analysis and Regression",
publisher = "Addison-Wesley",
address = "Reading, Massachusetts",
kwds = "book, stat, regr, exploratory data analysis"
}
@inproceedings{motz:52,
author = "T. S. Motzkin",
year = "1952",
title = "New Techniques for Linear Inequalities and Optimization",
booktitle = "Scientific Computation of Optimum Programs,
Symposium on Linear Inequalities and Programming",
editor = "",
pages = "15--27",
publisher = "Planning Research Division, Director of Management Analysis
Service, Comptroller, Headquarters U. S. Air Force",
address = "Washington, D.C.",
note = "Composed from notes taken at the symposium by Leon
Goldstein.",
kwds = "nlop, linear inequalities, iter"
}
-mp- -mq- -mr- -ms- -mt- -mu-
@article{muel:66,
author = "D. Mueller",
year = "1966",
title = "{H}ouseholder's Method for Complex Matrices and {H}ermitian
Matrices",
journal = "Numerische Mathematik",
volume = "8",
pages = "72--92",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, complex matrix, symmetric matrix"
}
@article{mull:56,
author = "D. E. Muller",
year = "1956",
title = "A Method for Solving Algebraic Equations using
an Automatic Computer",
journal = "Mathematical Tables and Other Aids to Computation",
volume = "10",
pages = "208--215",
kwds = "nlop, polynomial, Muller's method"
}
@article{mudg:89,
author = "R. R. Muntz, E. De Souza Silva, A. Goyal",
year = "1989",
title = "Bounding Availability of Reparable
Computer Systems",
journal = "IEE-TC",
volume = "",
pages = "",
note = "Cited in \cite{lumu:89}.",
kwds = "nla, Markov chain, queue"
}
@article{mupa:73,
author = "I. Munro and M. Patterson",
year = "1973",
title = "Optimal Algorithms for Parallel Polynomial Evaluation",
journal = "Journal of Computer and System Sciences",
volume = "7",
pages = "189--198",
kwds = "nlop, prll, polynomial, complexity"
}
@article{muwi:31,
author = "F. D. Murnaghan and A. Wintner",
year = "1931",
title = "A Canonical Form for Real Matrices under Orthogonal
Transformation",
journal = "Proc. Nat. Acad. Sci.",
volume = "17",
pages = "417-420",
kwds = "la, svd"
}
-mv- -mw- -mx- -my- -mz-
-na-
@techreport{nart:90,
author = "N. M. Nachtigal and L. Reichel and L. N. Trefethen",
year = "1990",
title = "A Hybrid {GMRES} Algorithm for Nonsymmetric Matrix
Iterations",
institution = "Department of Mathematics, Massachusetts Institute
of Technology",
type = "Numerical Analysis Report",
number = "90-7",
kwds = "nla, sparse, linear system, GMRES"
}
@article{nand:85,
author = "T. Nanda",
year = "1985",
title = "Differential Equations and the {QR} Algorithm",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "22",
pages = "310--321",
note = "Cited in \cite{govl:89}.",
kwds = "nla, QR algorithm, ode"
}
@article{nash:75,
author = "J. C. Nash",
year = "1975",
title = "A One-sided Transformation Method for the Singular Value
Decomposition and Algebraic Eigenproblem",
journal = "Computer Journal",
volume = "18",
pages = "74--76",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, svd, Jacobi-like"
}
@book{nash:76,
author = "M. Z. Nashed (ed)",
year = "1976",
title = "Generalized Inverses and Applications",
publisher = "Academic Press",
address = "New York",
kwds = "book, la, ginv"
}
@incollection{nara:76,
author = "M. Z. Nashed and L. B. Rall",
year = "1976",
title = "Annotated Bibliography on Generalized Inverses and Applications",
booktitle = "Generalized Inverses and Applications",
editor = "M. Z. Nashed",
publisher = "Academic Press",
address = "New York",
pages = "771-1041",
kwds = "la, ginv, bibliography"
}
@article{nasa:79,
author = "D. Nassimi and S. Sahni",
year = "1979",
title = "Bitonic Sort on a Mesh-Connected Parallel Computer",
journal = "IEEE Transactions on Computer",
volume = "C-27",
pages = "2--7",
kwds = "sorting, prll"
}
@article{nats:83,
author = "M. Natori and A. Tsukamoto",
year = "1983",
title = "A Fast Method for Estimating the Condition Number
of a Matrix",
journal = "Journal of Information Processing",
volume = "6",
pages = "138--140",
kwds = "nla, condition estimation"
}
@article{naza:80,
author = "L. Nazareth",
year = "1980",
title = "Some Recent Approaches to Solving Large Residual Nonlinear
Least Squares Problems",
journal = "SIAM Review",
volume = "22",
pages = "1--11",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
-nb- -nc- -nd- -ne-
@article{neme:65,
author = "J. A. Nelder and R. Mead",
year = "1965",
title = "A Simplex Method for Function Minimization",
journal = "Computer Journal",
volume = "8",
pages = "308--313",
kwds = "nlop"
}
@book{need:59,
author = "J. Needkam",
year = "1959",
title = "Science and Civilization in China",
publisher = "Cambridge University Press",
address = "Cambridge",
kwds = "book, history, China"
}
@article{neel:66,
author = "P. M. Neely",
year = "1966",
title = "Comparison of Several Algorithms for Computation of Means,
Standard Deviations, and Correlation Coefficients",
journal = "Communications of the ACM",
volume = "9",
pages = "496-499",
kwds = "mean, standard deviation, correlation, variance, updating"
}
@article{nesb:65,
author = "R. K. Nesbet",
year = "1965",
title = "Algorithm for Diagonalization of Large Matrices",
journal = "J. Chem. Phys.",
volume = "43",
pages = "311--312",
kwds = "nla, sparse, eig, relaxation, symmetric matrix"
}
@article{neum:85,
author = "A. Neumaier",
year = "1985",
title = "Residual Inverse Iteration for the Nonlinear
Eigenvalue Problem",
journal = "SIAM Journal on Numerical Analysis",
volume = "22",
pages = "914--923",
kwds = "nla, nlop, eig, inverse iteration"
}
@book{neum:1877,
author = "C. Neumann",
year = "1877",
title = "{Untersuchungen \"uber das logarithmische und Newtonische
Potential}",
address= "Leipzig",
kwds = "book, la, Neumann series"
}
@article{nepl:78,
author = "M. Neumann and R. J. Plemmons",
year = "1978",
title = "Convergent Nonnegative Matrices and Iterative Methods
for Consistent Linear Systems",
journal = "Numerische Mathematik",
volume = "31",
pages = "265--279",
kwds = "nla, Markov chain, iter, linear system, nonnegative matrix"
}
@article{nepl:79,
author = "M. Neumann and R. J. Plemmons",
year = "1979",
title = "Generalized Inverse-Positivity and Splittings of
{M}-Matrices",
journal = "Linear Algebra and Its Applications",
volume = "23",
pages = "21-35",
kwds = "nla, Markov chain, M-matrix, iter, ginv"
}
@article{newa:87,
author = "Heinz Neudecker and Tom Wansbeek",
year = "1987",
title = "Fourth-Order Properties of Normally Distributed
Random Matrices",
journal = "Linear Algebra and Its Applications",
volume = "97",
pages = "13-22",
kwds = "stat, la, random matrix"
}
@book{neut:81,
author = "M. Neuts",
year = "1981",
title = "Matrix-Geometric Solutions in Stochastic Models",
publisher = "Johns Hopkins University Press",
address = "Baltimore",
kwds = "book, nla, la, queue, matrix-geometric, Markov chain"
}
@incollection{newt:1669,
author = "Isaac Newton",
year = "1669?",
title = "{De Analysi per {\AE}quationes Infinitas}",
booktitle = "The Mathematical Papers of Isaac Newton, II",
editor = "D. T. Whiteside",
pages = "207--247",
publisher = "Cambridge University Press",
address = "Cambridge",
kwds = "na, history, Newton's method"
}
@incollection{newt:1670,
author = "Isaac Newton",
year = "1670--71?",
title = "{Tractatus de Methodis Serierum et Fluxionum}",
booktitle = "The Mathematical Papers of Isaac Newton, III",
editor = "D. T. Whiteside",
pages = "32--353",
publisher = "Cambridge University Press",
address = "Cambridge",
kwds = "na, history, Newton's method"
}
-nf- -ng-
@article{ng:91,
author = "E. Ng",
year = "1991",
title = "A Scheme for Handling Rank Deficiency in the Solution
of Sparse Linear Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "1173--1183",
note = "Citation communicated by Per Christian Hansen.",
kwds = "nla, lsq, sparse, rank determination"
}
-nh- -ni-
@article{nich:72,
author = "H. Nicholson",
year = "1972",
title = "Sequential Least-Squares Prediction Based on Spectral
Analysis",
journal = "Inernational J. Computer Math. Section B",
volume = "3",
pages = "247--270",
kwds = "stat, time series, lsq"
}
@article{nico:74,
author = "R. A. Nicolaides",
year = "1974",
title = "On a Geometrical Aspect of {SOR} and the Theory of Consistent
Ordering for Positive Definite Matrices",
journal = "Numerische Mathematik",
volume = "23",
pages = "99--104",
note = "Cited in \cite{govl:89}.",
kwds = "nla, relaxation, positive definite matrix"
}
@article{niva:83,
author = "W. Niethammer and R. S. Varga",
year = "1983",
title = "The Analysis of {$k$}-step Iterative Methods for Linear
Systems from Summability Theory",
journal = "Numerische Mathematik",
volume = "41",
pages = "177--206",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, iter"
}
@article{nipv:84,
author = "W. Niethammer and J. de Pillis and R. S. Varga",
year = "1984",
title = "Convergence of Block Iterative Methods Applied to Sparse
Least-squares Problems",
journal = "Linear Algebra and Its Applications",
volume = "58",
pages = "327--341",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, iter, lsq, sparse"
}
@article{nisb:72,
author = "R. M. Nisbet",
year = "1972",
title = "Acceleration of the Convergence in {Nesbet's} Algorithm
for Eigenvalues and Eigenvectors of Large Matrices",
journal = "Journal of Computational Physics",
volume = "10",
pages = "614--619",
kwds = "nla, eig, sparse, relaxation, symmetric matrix"
}
-nj- -nk- -nl- -nm- -nn- -no-
@book{nobl:69,
author = "B. Noble",
year = "1969",
title = "Applied Linear Algebra",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, la, nla"
}
@book{noda:77,
author = "B. Noble and J. W. Daniel",
year = "1977",
title = "Applied Linear Algebra",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, la, nla"
}
-np- -nq- -nr- -ns- -nt- -nu- -nv- -nw- -nx- -ny- -nz-
-oa- -ob-
@article{oben:77,
author = "R. L. Obenchain",
year = "1977",
title = "Classical {F}-Tests and Confidence Regions for Ridge
Regression",
journal = "Technometrics",
volume = "19",
pages = "429--439",
kwds = "stat, regr, ridge regression, hypothesis testing"
}
-oc- -od- -oe-
@article{oela:86,
author = "W. Oed and O. Lange",
year = "1986",
title = "Modelling, Measurement, and Simulation of Memory
Interference in the {CRAY XM-P}",
journal = "Parallel Computing",
volume = "3",
pages = "343-358",
kwds = "prll, vect, communication, contention, cray"
}
@article{oepr:64,
author = "W. Oettli and W. Prager",
year = "1964",
title = "Compatibility of Approximate Solution of Linear Equations
with Given Error Bounds for Coefficients and Right-Hand
Sides",
journal = "Numerische Mathematik",
volume = "6",
pages = "405--409",
kwds = "la, pert, linear system, backward perturbation"
}
-of- -og- -oh- -oi- -oj- -ok- -ol-
@phdthesis{olea:76,
author = "D. P. O'Leary",
year = "1976",
title = "Hybrid Conjugate Gradient Algorithms",
number = "STAN-CS-76-548",
school = "Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients"
}
@article{olsv:79,
author = "D. P. O'Leary and G. W. Stewart and J. S. Vandergraft",
year = "1979",
title = "Estimating the Largest Eigenvalue of a Positive Definite Matrix",
journal = "Mathematics of Computation",
volume = "33",
pages = "1289-1292",
kwds = "nla, eig, power method, symmetric matrix"
}
@article{olea:80,
author = "D. P. O'Leary",
year = "1980",
title = "A Generalized Conjugate Gradient Algorithm for Solving Class
of Quadratic Programming Problems",
journal = "Linear Algebra and Its Applications",
volume = "34",
pages = "371--399",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, conjugate gradients, quadratic programming"
}
@article{olea:80a,
author = "D. P. O'Leary",
year = "1980",
title = "Estimating Matrix Condition Numbers",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "1",
pages = "205--209",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, condition estimation"
}
@article{olea:80b,
author = "D. P. O'Leary",
year = "1980",
title = "The Block Conjugate Gradient Algorithm and Related Methods",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "293--322",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, block algorithm"
}
@article{olsi:81,
author = "D. P. O'Leary and J. A. Simmons",
year = "1981",
title = "A Bidiagonalization-Regularization Procedure for Large Scale
Discretizations of Ill-Posed Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "474--489",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, bidiagonalization, ill-posed problem, regularization"
}
@article{olst:85,
author = "D. P. O'Leary and G. W. Stewart",
year = "1985",
title = "Data-Flow Algorithms for Parallel Matrix Computations",
journal = "Communciations of the ACM",
volume = "28",
pages = "840-853",
kwds = "nla, prll, eig, Sylvester equation, Cholesky decomposition,
matrix equation"
}
@article{olwh:85,
author = "D. P. Oleary and R. E. White",
year = "1985",
title = "Multi-Splittings of Matrices and Parallel
Solution of Linear Systems",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "6",
pages = "630-640",
kwds = "nla, prll, linear system, pde"
}
@article{olst:86,
author = "D. P. O'Leary and G. W. Stewart",
year = "1986",
title = "Assignment and Scheduling in Parallel Matrix Factorization",
journal = "Linear Algebra and Its Applications",
volume = "28",
pages = "275-299",
kwds = "nla, prll, lud, Cholesky decomposition, communication,
message passing"
}
@techreport{olsv:86,
author = "D. P. O'Leary and G. W. Stewart and Robert van de Geijn",
year = "1986",
title = "{DOMINO}: A Message Passing Environment for
Parallel Computation",
institution = "University of Maryland, Computer Science",
type = "Technical Report",
number = "TR-1648",
kwds = "prll, message passing, operating system"
}
@techreport{opsw:86,
author = "D. P. O'Leary and Roger Pierson and
G. W. Stewart and Mark Wieser",
year = "1986",
title = "The {Maryland} {CRAB}:
A Module for Building Parallel Computers",
institution = "Department of Computer Science,
University of Maryland",
type = "Technical Report",
number = "TR-1660",
kwds = "prll, architecture, communication"
}
@article{olru:86,
author = "D. P. O'Leary and B. W. Rust",
year = "1986",
title = "Confidence Intervals for Inequality-Constrained Least Squares
Problems, with Applications to Ill-Posed Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "473--489",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, constraints, ill-posed problem, confidence interval"
}
@article{olea:87,
author = "D. P. O'Leary",
year = "1987",
title = "Parallel Implementation of the Block Conjugate Gradient
Algorithm",
journal = "Parallel Computing",
volume = "5",
pages = "127--139",
kwds = "prll, nla, conjugate gradients"
}
@article{olst:87,
author = "D. P. O'Leary and G. W. Stewart",
year = "1987",
title = "From Determinacy to Systaltic Arrays",
journal = "IEEE Transactions on Computers",
volume = "C-36",
pages = "1355-1359",
kwds = "prll, determinacy, message passing"
}
@article{olst:90,
author = "D. P. O'Leary and G. W. Stewart",
year = "1990",
title = "Computing the Eigenvalues and Eigenvectors
of Arrowhead Matrices",
journal = "Journal of Compuational Physics",
volume = "90",
pages = "497--505",
kwds = "nla, eig, symmetric matrix, arrowhead matrix"
}
@article{olea:90,
author = "D. P. O'Leary",
year = "1990",
title = "On Bounds For Scaled Projections and Pseudo-Inverses",
journal = "Linear Algebra and Its Applications",
volume = "132",
pages = "115--117",
kwds = "la, projection, ginv"
}
@article{olea:90a,
author = "D. P. O'Leary",
year = "1990",
title = "Robust Regression Computation Using Iteratively Reweighted
Least Squares",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "466--480",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, regr, robust estimation, lsq"
}
@article{olve:52,
author = "F. W. J. Olver",
year = "1952",
title = "The Evaluation of Zeros of High-Degree Polynomials",
journal = "Philosophical Transaction of the Royal Society of
London, Series A",
volume = "244",
pages = "385--415",
kwds = "nlop, polynomial"
}
@article{olve:78,
author = "F. W. J. Olver",
year = "1978",
title = "A New Approach to Error Arithmetic",
journal = "SIAM Journal on Numerical Analysis",
volume = "15",
pages = "368--393",
kwds = "na, rounding error"
}
-om- -on- -oo- -op- -oq- -or-
@techreport{orte:62,
author = "J. M. Ortega",
year = "1962",
title = "An Error Analysis of {Householder's} Method
for the Symmetric Eigenvalue Problem",
institution = "Applied Mathematics and Statistics Laboratories,
Stanford University",
type = "Technical Report",
number = "18",
kwds = "nla, eig, rounding error, Householder transformation,
symmetric matrix"
}
@article{orka:63,
author = "J. M. Ortega and H. F. Kaiser",
year = "1963",
title = "The {$LL^{\rm T}$} and {$QR$} Methods for Symmetric
Tridiagonal Matrices",
journal = "Computer Journal",
volume = "6",
pages = "99--101",
kwds = "nla, eig, tridiagonal matrix, QR algorithm, symmetric matrix"
}
@book{orrh:70,
author = "J. M. Ortega and W. C. Rheinboldt",
year = "1970",
title = "Iterative Solution of Nonlinear Equations in Several Variables",
publisher = "Academic Press",
address = "New York",
kwds = "book, nlop"
}
@article{orvo:85,
author = "J. M. Ortega and R. G. Voigt",
year = "1985",
title = "Solution of Partial Differential Equations on Vector and Parallel
Computers",
journal = "{SIAM} Review",
volume = "27",
pages = "149--240",
note = "Cited in \cite{govl:89}.",
kwds = "na, pde, vect, prll"
}
@article{orro:88,
author = "J. M. Ortega and C. H. Romine",
year = "1988",
title = "The {$ijk$} Forms of Factorization Methods {II}: Parallel Systems",
journal = "Parallel Computing",
volume = "7",
pages = "149--162",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, lud"
}
@techreport{orvr:90,
author = "J. M. Ortega and R. G. Voigt and C. H. Romine",
year = "1990",
title = "A Bibliography on Parallel and Vector Numerical Algorithms",
institution = "Oak Ridge National Laboratory",
type = "Technical Report",
number = "ORNL/TM-10998",
kwds = "prll, vect"
}
@book{orte:88,
author = "J. M. Ortega",
year = "1988",
title = "Introduction to Parallel and Vector Computing",
publisher = "Plenum Press",
address = "New York",
kwds = "book, prll, vect, linear system"
}
@techreport{orvr:89,
author = "J. M. Ortega and R. G. Voigt and C. H. Romine",
year = "1989",
title = "A Bibliography on Parallel and Vector Numerical Algorithms",
institution = "Oak Ridge National Laboratory",
type = "Technical Report",
number = "TM-10998",
kwds = "nla, prll, vect, bibliography"
}
-os-
@article{osbo:60,
author = "E. E. Osborne",
year = "1960",
title = "On Preconditioning of Matrices",
journal = "Journal of the {ACM}",
volume = "7",
pages = "338--345",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning, scaling"
}
@article{osbo:61,
author = "E. E. Osborne",
year = "1961",
title = "On Least Squares Solutions of Linear Equations",
journal = "Journal of the ACM",
volume = "8",
pages = "628--636",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, linear system, least squares"
}
@article{osbo:76a,
author = "E. E. Osborne",
year = "1976",
title = "Nonlinear Least Squares---the {Levenberg} Algorithm Revisited",
journal = "Journal of the Australian Mathematical Society, Series B",
volume = "19",
pages = "343--357",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Levenberg-Marquardt damping"
}
@article{osbo:74,
author = "M. R. Osborne",
year = "1974",
title = "Asymptotic Error Formula for Numerical Quadrature",
journal = "J. Inst. Maths Applics",
volume = "13",
pages = "219--227",
kwds = "na, numerical integration"
}
@article{osbo:76,
author = "M. R. Osborne",
year = "1976",
title = "On the Computation of Stepwise Regressions",
journal = "The Australian Computer Journal",
volume = "8",
pages = "61--63",
kwds = "stat, nla, regr, stepwise regression"
}
@incollection{osbo:76b,
author = "M. R. Osborne",
year = "1976",
title = "Some Aspects of Nonlinear Least Squares Calculations",
booktitle = "Numerical Methods for Nonlinear Optimization",
editor = "F.A. Lootsma",
pages = "171--189",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@book{osbo:85,
author = "M. R. Osborne",
year = "1985",
title = "Finite Algorithms in Optimization and Data Analysis",
publisher = "John Wiley \& Sons",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, nlop, lsq, nllsq"
}
@article{ostr:87,
author = "G. Ostrouchov",
year = "1987",
title = "Symbolic {Givens} Reduction and Row-Ordering in Large Sparse
Least Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "248--264",
kwds = "nla, qrd, lsq, plane rotation, sparse"
}
@article{ostr:36,
author = "A. M. Ostrowski",
year = "1936",
title = "{Konvergenzdiskussion und Fehlerabshc\"atzung f\"ur die
Newton'sche Methode bei Gleichungssystemen}",
journal = "Comentarii Mathematici Helvetici",
volume = "",
pages = "79--103",
kwds = "nlop, Newton's method"
}
@article{ostr:37,
author = "A. M. Ostrowski",
year = "1937",
title = " {\"Uber die Determinanten mit \"Uberwiegender Hauptdiagonale}",
journal = "Commentarii Mathematici Helvetici",
volume = "10",
pages = "69--96",
kwds = "la, eig, ovals of Cassini, determinant"
}
@article{ostr:39,
author = "A. M. Ostrowski",
year = "1939",
title = "Sur la continuit\'e relative des racines d'\'equations
alg\'egriques",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "209",
pages = "777--779",
kwds = "nlop, polynomial, pert"
}
@article{ostr:40,
author = "A. M. Ostrowski",
year = "1940",
title = " {Researches sur la m\'ethode de Graeffe et les z\'eros
des polynomials et des s\'eries de Laurent}",
journal = "Acta Mathematica",
volume = "72",
pages = "99--257",
kwds = "nlop, Graeffe's method, pert, polynomial"
}
@article{ostr:51,
author = "A. M. Ostrowski",
year = "1951",
title = "{Ueber das Nichtverschwinden einer Klasse von Determinanten
und die Lokalisierung der charakteristischen Wurzel von
Matrizen}",
journal = "Compositio Mathematica",
volume = "9",
pages = "209--226",
kwds = "la, eig, pert, ovals of Cassini, determinant"
}
@article{ostr:52,
author = "A. M. Ostrowski",
year = "1952",
title = "Sur quelques applications des fonctions convexes
et concaves au sens de {I. Schur}",
journal = " {Journal de Math\'ematiques Pures et Appliqu\'ees}",
volume = "117",
pages = "253--292",
kwds = "la, majorization"
}
@article{ostr:56,
author = "A. M. Ostrowski",
year = "1956",
title = "{Zur relativen Stetigkeit von Wurzeln algebraischer
Gleichungen}",
journal = "Jahresberichte der Deutsche Mathematische Verein",
volume = "58",
pages = "98--102",
kwds = "la, pert, eig"
}
@article{ostr:57,
author = "A. M. Ostrowski",
year = "1957",
title = " {\"Uber die Stetigkeit von charakteristischen Wurzeln in
Abh\"angigkeit von den Matrizenelementen}",
journal = "Jahresberichte der Deutsche Mathematische Verein",
volume = "60",
pages = "40--42",
kwds = "la, pert, eig"
}
@article{ostr:58,
author = "A. M. Ostrowski",
year = "1958",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {I}",
journal = "Arch. Rational Mech. Anal.",
volume = "1",
pages = "233--241",
kwds = "nla, eig, Rayleigh quotient"
}
@article{ostr:58a,
author = "A. M. Ostrowski",
year = "1958",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {II}",
journal = "Arch. Rational Mech. Anal.",
volume = "2",
pages = "423--428",
kwds = "nla, eig, Rayleigh quotient"
}
@article{ostr:59,
author = "A. M. Ostrowski",
year = "1959",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {III} (Generalizd {Rayleigh} Quotient and
Characteristic Roots with Linear Elementary Divisors)",
journal = "Arch. Rational Mech. Anal.",
volume = "3",
pages = "325--240",
kwds = "nla, eig, Rayleigh quotient"
}
@article{ostr:59a,
author = "A. M. Ostrowski",
year = "1959",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {IV} (Generalized {Rayleigh} Quotient for
Nonlinear Elementary Divisors)",
journal = "Arch. Rational Mech. Anal.",
volume = "3",
pages = "341--347",
kwds = "nla, eig, Rayleigh quotient"
}
@article{ostr:59b,
author = "A. M. Ostrowski",
year = "1959",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {V} (Usual {Rayleigh} Quotient for Non-{Hermitian}
Matrices and Linear Elementary Divisors)",
journal = "Arch. Rational Mech. Anal.",
volume = "3",
pages = "472--481",
kwds = "nla, eig, Rayleigh quotient"
}
@article{ostr:59c,
author = "A. M. Ostrowski",
year = "1959",
title = "On the Convergence of the {Rayleigh} Quotient Iteration
for the Computation of the Characteristic Roots
and Vectors. {VI} (Usual {Rayleigh} Quotient for Nonlinear
Elementary Divisors)",
journal = "Arch. Rational Mech. Anal.",
volume = "4",
pages = "153--165",
kwds = "nla, eig, Rayleigh quotient"
}
@techreport{ostr:66,
author = "A. M. Ostrowski",
year = "1966",
title = "On Clusters of Roots of Polynomial Equations",
institution = "University of Wisconson, Mathematics Research Center",
type = "Technical Summary Report",
number = "629",
kwds = "nlop, polynomial, pert"
}
-ot- -ou-
@article{ouel:81,
author = "D. V. Ouellette",
year = "1981",
title = "{Schur} Complement and Statistics",
journal = "Linear Algebra and its Applications",
volume = "36",
pages = "187-295",
kwds = "math, stat, la, Schur complement"
}
-ov- -ow- -ox- -oy- -oz-
-pa-
@article{paar:71,
author = "M. H. C. Paardekooper",
year = "1971",
title = "An Eigenvalue Algorithm for Skew Symmetric Matrices",
journal = "Numerische Mathematik",
volume = "17",
pages = "189--202",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, skew-symmetric matrix"
}
@techreport{paar:79,
author = "M. Paardekooper",
year = "1979",
title = "Inverse Perturbations for Approximations of Least
Squares Solutions",
institution = "Katholieke Hogeschool Tilburg, Faculteit der
Economische Wetenschappen",
type = "Technical Report",
number = "79.083",
kwds = "nla, lsq, pert, backward perturbation"
}
@article{pawo:87,
author = "Edward W. Packel and Hynryk Wo\'zniakowski",
year = "1987",
title = "Recent Developments in Information-Based Complexity",
journal = "Bulliten of the American Mathematical Society",
volume = "17",
pages = "9-36",
kwds = "math, nla, complexity, eig"
}
@article{page:81,
author = "M. D. Pagel",
year = "1981",
title = "Comment on {Hoerl} and {Kennard's} Ridge Regression Simulation
Methodology",
journal = "Communications in Statistics Theory and Methods",
volume = "A10",
pages = "2361-2367",
kwds = "stat, regr, ridge regression"
}
@article{paig:70,
author = "C. C. Paige",
year = "1970",
title = "Practicle Use of the Symmetric Lanczos Process with
Reorthogonalization",
journal = "BIT",
volume = "10",
pages = "183--195",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix, sparse"
}
@phdthesis{paig:71,
author = "C. C. Paige",
year = "1971",
title = "The Computation of Eigenvalues and Eigenvectors of
Very Large Sparse Matrices",
school = "University of London",
kwds = "nla, eig, pert, Lanczos algorithm, sparse"
}
@article{paig:72,
author = "C. C. Paige",
year = "1972",
title = "Computational Variants of the Lanczos Method for the
Eigenproblem",
journal = "J. Inst. Math. Appl.",
volume = "10",
pages = "373--381",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix, sparse"
}
@article{paig:73,
author = "C. C. Paige",
year = "1973",
title = "An Error Analysis of a Method for Solving Matrix Equations",
journal = "Mathematics of Computation",
volume = "27",
pages = "355--359",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, underdetermined system, rounding error"
}
@article{paig:74,
author = "C. C. Paige",
year = "1974",
title = "Bidiagonalization of Matrices and Solution of Linear Equations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "197--209",
note = "Cited in \cite{govl:89}.",
kwds = "nla, bidiagonalization, linear system, sparse, indefinite system"
}
@article{paig:74b,
author = "C. C. Paige",
year = "1974",
title = "Eigenvalues of Perturbed {H}ermitian Matrices",
journal = "Linear Algebra and its Applications",
volume = "8",
pages = "1--10",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, eig, symmetric matrix"
}
@article{pasa:75,
author = "C. C. Paige and M. A. Saunders",
year = "1975",
title = "Solution of Sparse Indefinite Systems of Linear
Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "617--629",
kwds = "nla, sparse, Lanczos algorithm, linear system, indefinite system"
}
@article{pasw:75,
author = "C. C. Paige and G. P. H. Styan and P. G. Wachter",
year = "1975",
title = "Computation of the Stationary Distribution of a
{Markov} Chain",
journal = "J. Statistc. Comput. Simul.",
volume = "4",
pages = "173--186",
kwds = "nla, eig, Markov chain"
}
@article{paig:76,
author = "C. C. Paige",
year = "1976",
title = "Error Analysis of the {Lanczos} Algorithm for Tridiagonalizing
a Symmetric Matrix",
journal = "J. Inst. Math. Applics.",
volume = "18",
pages = "341--349",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Lanczos algorithm, rounding error, symmetric matrix"
}
@article{pasa:77,
author = "C. C. Paige and M. A. Saunders",
year = "1977",
title = "Least Squares Estimation of Discrete Linear Dynamic Systems
Using Orthogonal Transformations",
journal = "SIAM Journal on Numerical Analysis",
volume = "14",
pages = "180--193",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, control, qrd"
}
@article{paig:78,
author = "C. C. Paige",
year = "1978",
title = "Numerically Stable Computations for General
Univariate Linear Models",
journal = "Communications in Statistics",
volume = "B7",
pages = "437--453",
kwds = "stat, nla, regr, lsq, updating"
}
@techreport{pasa:78,
author = "C. C. Paige and M. A. Saunders",
year = "1978",
title = "A Bidiagonalization Algorithm for Sparse Linear Equations and
Least Squares Problems",
number = "SOL 78-19",
institution = "Operations Research, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, lsq, bidiagonalization, linear system,
sparse"
}
@article{paig:79,
author = "C. C. Paige",
year = "1979",
title = "Computer Solution and Perturbation Analysis of
Generalized Linear Least Squares Problems",
journal = "Mathematics of Computation",
volume = "33",
pages = "171-184",
kwds = "nla, regr, pert, lsq, generalized least squares, pert"
}
@article{paig:79a,
author = "C. C. Paige",
year = "1979",
title = "Fast Numerically Stable Computations for Generalized
Least Squares Problems",
journal = "SIAM J. on Numerical Analysis",
volume = "16",
pages = "165--171",
kwds = "nla, lsq"
}
@article{paig:80,
author = "C. C. Paige",
year = "1980",
title = "Error Analysis of Some Techniques for Updating Orthogonal
Decompositions",
journal = "Mathematics of Computation",
volume = "34",
pages = "465-471",
kwds = "math, nla, qrd, updating, rounding error"
}
@article{paig:80a,
author = "C. C. Paige",
year = "1980",
title = "Accuracy and Effectiveness of the {L}anczos Algorithm for the
Symmetric Eigenproblem",
journal = "Linear Algebra and its Applications",
volume = "34",
pages = "235--258",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm, rounding error"
}
@article{paig:81,
author = "C. C. Paige",
year = "1981",
title = "Properties of Numerical Algorithms Related to
Computing Controllability",
journal = "IEEE Trans. Automatic Control",
volume = "26",
pages = "130--138",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, control"
}
@article{pavl:81,
author = "C. C. Paige and Van Loan, C.",
year = "1981",
title = "A {S}chur Decomposition for {H}amiltonian Matrices",
journal = "Linear Algebra and its Applications",
volume = "41",
pages = "11--32",
note = "Cited in \cite{govl:89}.",
kwds = "la, J-symmetric matrix, Schur form"
}
@article{pasa:81,
author = "C. C. Paige and M. A. Saunders",
year = "1981",
title = "Toward a Generalized Singular Value Decomposition",
journal = "SIAM Journal on Numerical Analysis",
volume = "18",
pages = "398-405",
kwds = "math, la, gsvd, csd"
}
@article{pasa:82,
author = "C. C. Paige and M. A. Saunders",
year = "1982",
title = "{LSQR}. An Algorithm for Sparse Linear Equations and Sparse
Least Squares",
journal = "ACM Transactions on Mathematical Software",
volume = "8",
pages = "43--71",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, conjugate gradients, Lanczos algorithm"
}
@article{pasa:82a,
author = "C. C. Paige and M. A. Saunders",
year = "1982",
title = "Algorithm 583 {LSQR}: Sparse Linear Equations and Sparse
Least Squares",
journal = "ACM Transactions on Mathematical Software",
volume = "8",
pages = "195--209",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, conjugate gradients, Lanczos algorithm, software"
}
@article{paig:84,
author = "C. C. Paige",
year = "1984",
title = "A Note on a Result of {Sun Ji-guang}: Sensitivity of the
CS and GSV Decomposition",
journal = "SIAM Journal on Numerical Analysis",
volume = "21",
pages = "186-191",
kwds = "nla, pert, svd, gsvd"
}
@article{paig:85,
author = "C. C. Paige",
year = "1985",
title = "The General Linear Model and the Generalized Singular Value
Decomposition",
journal = "Linear Algebra and its Applications",
volume = "70",
pages = "269--284",
note = "Cited in \cite{govl:89}.",
kwds = "nla, stat, svd, general linear model"
}
@article{paig:86,
author = "C. C. Paige",
year = "1986",
title = "Computing the Generalized Singular Value Decomposition",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "7",
pages = "1126--1146",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, gsvd, Jacobi-like"
}
@article{pavd:86,
author = "C. C. Paige and Van Dooren, P.",
year = "1986",
title = "On the Quadratic Convergence of {K}ogbetliantz's Algorithm for
Computing the Singular Value Decomposition",
journal = "Linear Algebra and its Applications",
volume = "77",
pages = "301--313",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Kogbetliantz's algorithm, svd, Jacobi-like"
}
@inproceedings{paig:90,
author = "C. C. Paige",
year = "1990",
title = "Some Aspects of Generalized {QR} Factorizations",
pages = "71--91",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. J. Hammarling",
publisher = "Clarendon Press",
address = "Oxford",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, generalized QR decomposition"
}
@phdthesis{pan:87,
author = "Ching-Tsuan Pan",
year = "1987",
title = "Hyperbolic Rotations for Downdating the {Cholesky}
Factorization with Applications to Signal Processing",
school = "Department of Mathematics, North Carolina State University",
kwds = "math, nla, lud, Cholesky decomposition, updating,
hyperbolic transformation"
}
@article{pan:84,
author = "V. Pan",
year = "1984",
title = "How Can We Speed Up Matrix Multiplication?",
journal = "{SIAM} Review",
volume = "26",
pages = "393--416",
note = "Cited in \cite{govl:89}.",
kwds = "la, nla, fast algorithm, matrix multiplication"
}
@book{pan:84a,
author = "V. Pan",
year = "1984",
title = "How to Multiply Matrices Faster",
publisher = "Springer",
address = "New York",
kwds = "book, la, nla, fast algorithm, matrix multiplication"
}
@article{pasc:91,
author = "V. Pan and R. Schreiber",
year = "1991",
title = "An Improved Newton Iteration for the Generalized Inverse
of a Matrix with Applications",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "12",
pages = "1109--1130",
kwds = "nla, inverse matrix, ginv, Newton's method"
}
@unpublished{park:91,
author = "H. Park",
year = "1991",
title = "{ESPRIT} Direction-of-Arrival Estimation in the Presence
of Spatially Correlated Noise",
note = "Computer Science Department, University of Minnesota.
AHPCRC Preprint 91--08",
kwds = "nla, signal processing, direction of arrival, esprit"
}
@article{parl:64,
author = "B. N. Parlett",
year = "1964",
title = "{Laguerre's} Method Applied to the Matrix Eigenvalue Problem",
journal = "Mathematics of Computation",
volume = "18",
pages = "464--485",
kwds = "nla, eig, Laguerre's method, polynomial"
}
@article{parl:65,
author = "B. N. Parlett",
year = "1965",
title = "Convergence of the {QR}~Algorithm",
journal = "Numerische Mathematik",
volume = "7",
pages = "187--193",
kwds = "nla, eig, QR algorithm"
}
@article{parl:65,
author = "B. N. Parlett",
year = "1965",
title = "Convergence of the {QR} Algorithm",
journal = "Numerische Mathematik",
volume = "7",
pages = "187--193",
note = "Correction in Numerische Mathematik 10, pp. 163--164",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, QR algorithm"
}
@article{parl:66,
author = "B. N. Parlett",
year = "1966",
title = "Singular and Invariant Matrices Under the {QR} Algorithm",
journal = "Mathematics of Computation",
volume = "20",
pages = "611--615",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, QR algorithm"
}
@article{parl:68,
author = "B. N. Parlett",
year = "1968",
title = "Global Convergence of the Basic {QR}~Algorithm
on Hessenberg Matrices",
journal = "Mathematics of Computation",
volume = "22",
pages = "803--817",
kwds = "nla, eig, QR algorithm, Hessenberg matrix"
}
@article{pare:69,
author = "B. N. Parlett and C. Reinsch",
year = "1969",
title = "Balancing a Matrix for Calculation of Eigenvalues
and Eigenvectors",
journal = "Numerische Mathematik",
volume = "13",
pages = "293--304",
note = "Also in \cite[pp.315--326]{wire:71}.",
kwds = "nla, eig, scaling, software"
}
@article{pare:70,
author = "B. N. Parlett and J. K. Reid",
year = "1970",
title = "On the Solution of a System of Linear Equations Whose
Matrix is Symmetric but not Definite",
journal = "BIT",
volume = "10",
pages = "386--397",
kwds = "nla, linear system, indefinite system, symmetric matrix"
}
@article{parl:71,
author = "B. N. Parlett",
year = "1971",
title = "Analysis of Algorithms for Reflections in Bisectors",
journal = "SIAM Review",
volume = "13",
pages = "197--208",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, Householder transformation, rounding error"
}
@article{papo:73,
author = "B. N. Parlett and W. G. Poole",
year = "1973",
title = "A Geometric Theory for the {QR}, {LU}, and Power Iterations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "10",
pages = "389--412",
note = "Cited in \cite{govl:89}.",
kwds = "nla, QR algorithm, power method, eig"
}
@techreport{parl:74,
author = "B. N. Parlett",
year = "1974",
title = "Computation of Functions of Triangular Matrices",
type = "Memorandum",
number = "ERL-M481",
institution = "Electronics Research Laboratory, College of Engineering,
University of California, Berkeley",
address = "Berkeley, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, triangular matrix"
}
@article{parl:74,
author = "B. N. Parlett",
year = "1974",
title = "The {R}ayleigh Quotient Iteration and Some Generalizations for
Nonnormal Matrices",
journal = "Mathematics of Computation",
volume = "28",
pages = "679--693",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Rayleigh quotient, nonnormal matrix"
}
@article{pawa:75,
author = "B. N. Parlett and Y. Wang",
year = "1975",
title = "The Influence of the Compiler on the Cost of
Mathematical Software---in Particular on the Cost
of Triangular Factorization",
journal = "ACM Transactions on Mathematical Software",
volume = "1",
pages = "35--46",
kwds = "nla, cs, software, lud"
}
@article{parl:76,
author = "B. N. Parlett",
year = "1976",
title = "A Recurrence Among the Elements of Functions of Triangular
Matrices",
journal = "Linear Algebra and its Applications",
volume = "14",
pages = "117--121",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, triangular matrix"
}
@article{parl:79,
author = "B. N. Parlett",
year = "1979",
title = "The {Lanczos} Algorithm with Selective Orthogonalization",
journal = "Mathematics of Computation",
volume = "22",
pages = "217--238",
kwds = "nla, eig, Lanczos algorithm, sparse, orthogonalization"
}
@article{pasc:79,
author = "B. N. Parlett and D. S. Scott",
year = "1979",
title = "The {L}anczos Algorithm with Selective Orthogonalization",
journal = "Mathematics of Computation",
volume = "33",
pages = "217--238",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos Algorithm, orthogonalization"
}
@book{parl:80,
author = "B. N. Parlett",
year = "1980",
title = "The Symmetric Eigenvalue Problem",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, math, la, nla, eig, symmetric matrix"
}
@article{parl:80a,
author = "B. N. Parlett",
year = "1980",
title = "A New Look at the {L}anczos Algorithm for Solving Symmetric Systems
and Linear Equations",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "323--346",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, symmetric matrix, linear system"
}
@article{pare:81,
author = "B. N. Parlett and J. K. Reid",
year = "1981",
title = "Tracking the Progress of the {L}anczos Algorithm for
Large Symmetric Eigenproblems",
journal = "{IMA} Journal of Numerical Analysis",
volume = "1",
pages = "135--155",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, eig, sparse"
}
@article{pass:82,
author = "B. N. Parlett and H. Simon and L. M. Stringer",
year = "1982",
title = "On Estimating the Largest Eigenvalue with the
{Lanczos} Algorithm",
journal = "Mathematics of Computation",
volume = "38",
pages = "153--165",
kwds = "nla, eig, Lanczos algorithm"
}
@article{pala:82,
author = "B. N. Parlett and T. L. Landis",
year = "1982",
title = "Methods for Scaling to Double Stochastic Form",
journal = "Linear Algebra and Its Applications",
volume = "48",
pages = "53--79",
kwds = "nla, eig, nonnegative matrix, doubly stochastic matrix"
}
@incollection{parl:82,
author = "B. N. Parlett",
year = "1982",
title = "Two Monitoring Schemes for the {Lanczos} Algorithm",
booktitle = "Computer Methods in Applied Sciences and
Engineering, V",
editor = "R. Glowinski and J. L. Liona",
publisher = "North-Holland",
address = "Amsterdam",
kwds = "nla, eig, Lanczos algorithm"
}
@article{parl:82a,
author = "B. N. Parlett",
year = "1982",
title = "Winograd's {Fourier} Transform via Circulants",
journal = "Linear Algebra and Its Applications",
volume = "45",
pages = "137--155",
kwds = "na, nla, eig, fft, fast algorithm, circulant matrix"
}
@article{pano:85,
author = "B. N. Parlett and B. Nour-Omid",
year = "1985",
title = "The Use of a Refined Error Bound When Updating Eigenvalues of
Tridiagonals",
journal = "Linear Algebra and its Applications",
volume = "68",
pages = "179--220",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, pert, tridiagonal matrix"
}
@unpublished{parl:90,
author = "B. N. Parlett",
year = "1990",
title = "Symmetric Matrix Pencils",
note = "Prepared for the International
Symposium on Mathematics of Computation, Ehime
University, Matsuyama, Japan. Manuscript.
Mathematics Department, University of
California, Berkeley",
kwds = "la, geig, Rayleigh quotient, matrix pencil, symmetric matrix"
}
@article{part:61,
author = "S. V. Parter",
year = "1961",
title = "The Use of Linear Graphs in {Gauss} Elimination",
journal = "SIAM Review",
volume = "3",
pages = "119--130",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, lud"
}
@book{parz:60,
author = "E. Parzen",
year = "1960",
title = "Modern Probability Theory and Its Applications",
publisher = "John Wiley",
address = "New York",
kwds = "book, math, probability"
}
@article{pajo:84,
author = "N. Patel and H. Jordan",
year = "1984",
title = "A Parallelized Point Rowwise Successive Over-Relaxation Method on
a Multiprocessor",
journal = "Parallel ",
volume = "1",
pages = "207--222",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, relaxation, linear system"
}
@article{past:73,
author = "M. S. Paterson and L. J. Stockmeyer",
year = "1973",
title = "On the Number of Nonscalar Multiplications Necessary to Evaluate
Polynomials",
journal = "{SIAM} Journal on Computing",
volume = "2",
pages = "60--66",
note = "Cited in \cite{govl:89}.",
kwds = "na, polynomial, complexity"
}
@inproceedings{papa:69,
author = "M. Pavel-Parvu and A. Korganoff",
year = "1969",
title = "Iteration Functions for Solving Polynomial Equations",
booktitle = "Constructive Aspects of the Fundamental Theorem of Algebra",
editor = "B. Dejon and P. Henrici",
pages = "",
publisher = "John Wiley",
address = "New York",
kwds = "la, ginv, matrix derivative"
}
@book{pare:82,
author = "J. K. Patel and C. B. Read",
year = "1982",
title = "Handbook of the Normal Distribution",
publisher = "Marcle Dekker",
address = "New York",
kwds = "book, stat, distribution"
}
-pb- -pc- -pd- -pe-
@article{pean:1888,
author = "G. Peano",
year = "1888",
title = "Int\'egration par s\'eries des \'equations diff\'erentielles
lin\'eaires",
journal = "Mathematische Annallen",
volume = "32",
pages = "450-456",
kwds = "math, svd, ode"
}
@article{pear:01,
author = "K. Pearson",
year = "1901",
title = "On Lines and Planes of Closest Fit to Points in Space",
journal = "Philosophical Magazine",
volume = "2",
pages = "559--572",
note = "Cited in \cite{govl:89}.",
kwds = "stat, svd, total least squares"
}
@article{peas:67,
author = "M. C. Pease",
year = "1967",
title = "Matrix Inversion Using Parallel Processing",
journal = "Journal of the ACM",
volume = "14",
pages = "757--764",
kwds = "nla, prll, lud, linear system, inverse matrix"
}
@article{peso:40,
author = "A. Pellew and R. U. Southwell",
year = "1940",
title = "Relaxation Methods Applied to Engineering Problems {VI}.
The Natural Frequencies of Systems Having Restricted
Degrees of Freedom",
journal = "Proc. Roy. Soc. (A)",
volume = "175",
pages = "262--290",
kwds = "nla, eig, relaxation, sparse"
}
@article{penr:55,
author = "R. Penrose",
year = "1955",
title = "A Generalized Inverse for Matrices",
journal = "Proceedings of the Cambridge Philosophical Society",
volume = "51",
pages = "406-413",
kwds = "math, la, ginv"
}
@article{penr:56,
author = "R. Penrose",
year = "1956",
title = "On Best Approximate Solutions of Linear Matrix Equations",
journal = "Proceedings of the Cambridge Philosophical Society",
volume = "52",
pages = "17-19",
kwds = "math, la, lsq, ginv"
}
@article{pepe:83,
author = "G. M. Peponides and P. K. Kokotovic",
year = "1983",
title = "Weak Connections, Time Scales, and Aggregation
of Nonlinear Systems",
journal = "IEEE Transactions on Circuits and Systems",
volume = "30",
pages = "416--422",
kwds = "nlop, aggregation"
}
@article{pere:67,
author = "V. Pereyra",
year = "1967",
title = "Iterative Methods for Solving Nonlinear Least
Squares Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "4",
pages = "27--36",
kwds = "nlop, lsq, ginv, nllsq"
}
@article{pere:69,
author = "V. Pereyra",
year = "1969",
title = "Stability of General Systems of Linear Equations",
journal = "Aequationes Mathematicae",
volume = "2",
pages = "194--206",
kwds = "la, pert, ginv"
}
@article{pewi:69,
author = "G. Peters and J. H. Wilkinson",
year = "1969",
title = "Eigenvalue of {$Ax = \lambda Bx$} with Band Symmetric {$A$}
and {$B$}",
journal = "The Computer Journal",
volume = "12",
pages = "398--404",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, band matrix, symmetric matrix"
}
@article{pewi:70,
author = "G. Peters and J. H. Wilkinson",
year = "1970",
title = "The Least Squares Problem and Pseudo-Inverses",
journal = "The Computer Journal",
volume = "13",
pages = "309--316",
kwds = "nla, lsq, ginv"
}
@article{pewi:70a,
author = "G. Peters and J. H. Wilkinson",
year = "1970",
title = "Eigenvectors of Real and Complex Matrices by
{LR}~and {QR}~Triangularization",
journal = "Numerische Mathematik",
volume = "16",
pages = "181--204",
note = "Also in \cite[pp.372--395]{wire:71}.",
kwds = "nla, eig, complex matrix, nonsymmetric matrix, software"
}
@article{pewi:70b,
author = "G. Peters and J. H. Wilkinson",
year = "1970",
title = "{$Ax = \lambda Bx$} and the Generalized Eigenproblem",
journal = "SIAM Journal on Numerical Analysis",
volume = "7",
pages = "479--492",
kwds = "nla, geig"
}
@incollection{pewi:71,
author = "G. Peters and J. H. Wilkinson",
year = "1971",
title = "The Calculation of Specified Eigenvectors by Inverse
Iteration",
booktitle = "Linear Algebra",
editor = "J. H. Wilkinson and C. Reinsch",
pages = "418--439",
publisher = "Springer",
address = "New York",
kwds = "nla, eig, symmetric matrix, inverse iteration, tridiagonal matrix,
software"
}
@unpublished{pewi:73?,
author = "G. Peters and J. H. Wilkinson",
year = "1973?",
title = "Some Algorithms for the Solution of the Generalized
Symmetric Eigenvalue Problem {$Au=\lambda Bu$}",
note = "Manuscript",
kwds = "nla, geig, symmetric matrix"
}
@article{pewi:79,
author = "G. Peters and J. H. Wilkinson",
year = "1979",
title = "Inverse Iteration, Ill-Conditioned Equations, and
{N}ewton's Method",
journal = "{SIAM} Review",
volume = "21",
pages = "339--360",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, inverse iteration, ill-conditioned problem,
Newton's method"
}
-pf- -pg- -ph-
@article{phil:71,
author = "J. L. Phillips",
year = "1971",
title = "The Triangular Decomposition of {H}ankel Matrices",
journal = "Mathematics of Computation",
volume = "25",
pages = "599--602",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, Hankel matrix"
}
-pi-
@article{pica:09,
author = "\`E. Picard",
year = "1909",
title = "Quelques remarques sur les \'equations int\'egrales
de premi\`ere esp\`ece et sur certains probl\`ems
de {Physique math\'ematique}",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "148",
pages = "1563--1568",
kwds = "la, integral equation, svd, history"
}
@article{pica:10,
author = "\'E. Picard",
year = "1910",
title = "Sur un th{\'e}or{\`e}m g{\'e}n\'eral relatif aux {\'e}quations
int{\'e}grales de premi{\`e}r esp{\`e}ce et sur quelques
probl{\`e}mes de physique math{\'e}matique",
journal = "Rendicondi del Circolo Matematico di Palermo",
volume = "25",
pages = "79-97",
kwds = "la, norm, svd, integral equation, history"
}
@article{pipl:92,
author = "D. J. Pierce and R. J. Plemmons",
year = "1992",
title = "Fast Adaptive Condition Estimation",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "13",
pages = "274--291",
kwds = "nla, condition estimation, fast algorithm"
}
@inproceedings{pira:89,
author = "M. A. Pi\~nar and V. Ramirez",
year = "1989",
title = "Inversion of Toeplitz Matrices",
booktitle = "Orthogonal Polynomials and Their Applications",
editor = "J. Vinuesa",
pages = "171--177",
publisher = "Marcel Dekker",
address = "New York",
kwds = "orthogonal polynomial, Toeplitz matrix, inverse matrix"
}
-pj- -pk- -pl-
@article{plac:49,
author = "R. L. Plackett",
year = "1949",
title = "A Historical Note on the Method of Least Squares",
journal = "Biometrika",
volume = "36",
pages = "458-460",
kwds = "stat, lsq, history"
}
@article{plac:50,
author = "R. L. Plackett",
year = "1950",
title = "Some Theorems in Least Squares",
journal = "Biometrika",
volume = "37",
pages = "149-157",
kwds = "stat, lsq"
}
@article{plac:72,
author = "R. L. Plackett",
year = "1972",
title = "The Discovery of the Method of Least Squares",
journal = "Biometrika",
volume = "59",
pages = "239-251",
kwds = "stat, lsq, history"
}
@article{plem:72,
author = "R. J. Plemmons",
year = "1972",
title = "Monotonicity and Iterative Approximations Involving
Rectangular Matrices",
journal = "Mathematics of Computation",
volume = "26",
pages = "853--858",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, iter"
}
@article{plem:74,
author = "R. J. Plemmons",
year = "1974",
title = "Linear Least Squares by Elimination and {MGS}",
journal = "Journal of the ACM",
volume = "21",
pages = "581--585",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lud, lsq, Gram-Schmidt algorithm"
}
@article{plem:77,
author = "R. J. Plemmons",
year = "1977",
title = "{$M$}-Matrix Characterizations. {I}---Nonsingular {$M$}-Matrices",
journal = "Linear Algebra and Its Applications",
volume = "18",
pages = "175--188",
kwds = "la, M-matrix"
}
@article{plem:86,
author = "R. J. Plemmons",
year = "1986",
title = "A Parallel Block Iterative Scheme Applied to Computations in
Structural Analysis",
journal = "{SIAM} Journal on Algebraic and Discrete Methods",
volume = "7",
pages = "337--347",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, iter, block algorithm"
}
-pm- -pn-
@article{pnue:72,
author = "D. Pnueli",
year = "1972",
title = "Two Shift Theorems Leading to Lower Bounds to Eigenvalues",
journal = "Journal of Engineering Mathematics",
volume = "6",
pages = "47--51",
kwds = "nla, pert, eig"
}
-po-
@article{poly:50,
author = "G. Polya",
year = "1959",
title = "Remark on {Weyl's} Note ``{Inequalities} between the Two Kinds
of Eigenvalues of a Linear Transformation''",
journal = "Proceedings of the National Academy of Sciences",
volume = "36",
pages = "49--51",
kwds = "la, eig, svd"
}
@article{poly:69,
author = "B. T. Polyak",
year = "1969",
title = "The Conjugate Gradient Method in Extremal Problems",
journal = "USSR Computational Mathematics and Mathematical Physics",
volume = "7",
pages = "94--112",
kwds = "nla, conjugate gradients, sparse"
}
@techreport{pool:70,
author = "W. G. Poole",
year = "1970",
title = "A Geometric Convergence Theory for the {QR},
{Rayleigh} Quotient, and Power Iterations",
institution = "University of California, Berkeley",
type = "Technical Report",
number = "41",
kwds = "nla, QR algorithm, Rayleigh quotient, eig"
}
@article{poor:87,
author = "E. L. Poole and J. M. Ortega",
year = "1987",
title = "Multicolor {ICCG} Methods for Vector Computers",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "24",
pages = "1394--1418",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, vect, multicolor method"
}
@article{poto:57,
author = "D. A. Pope and C. Tompkins",
year = "1957",
title = "Maximizing Functions of Rotations: Experiments Concerning Speed of
Diagonalization of Symmetric Matrices Using {J}acobi's Method",
journal = "Journal of the {ACM}",
volume = "4",
pages = "459--466",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Jacobi's method"
}
@incollection{pojv:87,
author = "A. Pothen and S. Jha and U. Vemapulati",
year = "1987",
title = "Orthogonal Factorization on a Distributed Memory Multiprocessor",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = "{SIAM} Publications",
address = "Philadelphia, PA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, qrd, prll"
}
@techreport{pora:87,
author = "A. Pothen and P. Raghavan",
year = "1987",
title = "Distributed Orthogonal Factorization: {Givens}
and {Householder} Algorithms",
institution = "Computer Science Department, Pennsylvania
State University",
type = "Technical Report",
number = "CS-87-24",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, prll, Householder transformation, plane rotation"
}
@article{pofa:90,
author = "A. Pothen and C.-J. Fan",
year = "1990",
title = "Computing the Block Triangular Form of a Sparse Matrix",
journal = "ACM Trans.",
volume = "16",
pages = "303--324",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse"
}
@techreport{poth:91,
author = "A. Pothen",
year = "1991",
title = "Predicting the Structure of Sparse Orthogonal Factors",
institution = "Computer Science Department, Pennsylvania
State University",
type = "Technical Report",
number = "CS-91-27",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, Householder transformation"
}
@article{powe:62,
author = "M. J. D. Powell",
year = "1962",
title = "An Iterative Method for Finding Stationary Values of
a Function of Several Variables",
journal = "Computer Journal",
volume = "5",
pages = "147--151",
kwds = "nlop"
}
@article{powe:64,
author = "M. J. D. Powell",
year = "1964",
title = "An Efficient Method for Finding the Minimum of a Function
of Several Variables without Calculating Derivatives",
journal = "Computer Journal",
volume = "7",
pages = "155--162",
kwds = "nlop"
}
@article{powe:65,
author = "M. J. D. Powell",
year = "1965",
title = "A Method for Minimizing a Sum of Squares of Non-Linear
Functions without Calculating Derivatives",
journal = "Computer Journal",
volume = "8",
pages = "303--307",
kwds = "nlop, lsq, nllsq"
}
@inproceedings{pore:68,
author = "M. J. D. Powell and J. K. Reid",
year = "1968",
title = "On Applying {H}ouseholder's Method to Linear Least Squares
Problems",
booktitle = "Proceedings {IFIP} Congress",
pages = "122--126",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Householder transformation, lsq, qrd"
}
@article{powe:68,
author = "M. J. D. Powell",
year = "1968",
title = "On the Calculation of Orthogonal Vectors",
journal = "Computer Journal",
volume = "11",
pages = "302--304",
kwds = "nla, qrd, updating, orthogonalization"
}
@article{powe:69,
author = "M. J. D. Powell",
year = "1969",
title = "A Theorem on Rank One Modifications to a Matrix and
Its Inverse",
journal = "Computer Journal",
volume = "12",
pages = "288-290",
kwds = "nla, updating, inverse matrix"
}
@inproceedings{pore:69,
author = "M. J. D. Powell and J. K. Reid",
year = "1965",
title = "On Applying {Householder's} Method to
Linear Least Squares Problems",
booktitle = "Proceedings of the IFIP Congress 68",
editor = "A. J. M. Morell",
pages = "122--126",
publisher = " North Holland",
address = "Amsterdam",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, weights, Householder transformation"
}
@article{powe:70,
author = "M. J. D. Powell",
year = "1970",
title = "A Survey of Numerical Methods for Unconstrained Optimization",
journal = "SIAM Review",
volume = "12",
pages = "79--97",
kwds = "nlop"
}
@article{powe:71,
author = "M. J. D. Powell",
year = "1971",
title = "On the Convergence of the Variable Metric Algorithm",
journal = "J. Inst. Maths. Applics.",
volume = "7",
pages = "21--36",
kwds = "nlop, quasi-Newton, Davidon's method"
}
-pp- -pq- -pr-
@article{prch:91,
author = "S. Prasac and B. Chandna",
year = "1991",
title = "Direction-of-Arrival Estimation Using Rank Revealing
{QR}~Factorization",
journal = "IEEE Transactions on Signal Processing",
volume = "39",
pages = "1224--1229",
note = "Citation communicated by Per Christian Hansen.",
kwds = "signal processing, nla, qrd, rank determination,
direction of arrival"
}
@article{pryc:84,
author = "J. D. Pryce",
year = "1984",
title = "A New Measure of Relative Error for Vectors",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "21",
pages = "202--221",
note = "Cited in \cite{govl:89}.",
kwds = "nla, pert, relative error"
}
@article{pryc:85,
author = "J. D. Pryce",
year = "1985",
title = "Multiplicative Error Analysis of Matrix Transformation Algorithms",
journal = "{IMA} Journal of Numerical Analysis",
volume = "5",
pages = "437--445",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error"
}
-ps- -pt-
@article{ptak:92,
author = "V. Ptak",
year = "1992",
title = "Infinite Companion Matrices",
journal = "Linear Algebra and Its Applications",
volume = "166",
pages = "65--95",
kwds = "la, companion matrix"
}
-pu-
@article{pusc:90,
author = "H. Puschmann",
year = "1990",
title = "{Weitere unzul\"assige Abwandlungen der Vermutung
von Wilkinson}",
journal = "Linear Algebra and Its Applications",
volume = "141",
pages = "75--78",
kwds = "nla, lud, pivoting"
}
-pv- -pw- -px- -py-
@article{pyle:67,
author = "L. D. Pyle",
year = "1967",
title = "A Generalized Inverse $\epsilon$-Algorithm
for Constructing Intersection Projection Matrices with
Applications",
journal = "Numerische Mathematik",
volume = "10",
pages = "86--102",
kwds = "nla, ginv, projection"
}
-pz-
-qa- -qb- -qc- -qd- -qe- -qf- -qg- -qh- -qi-
@article{qi:84,
author = "L. Qi",
year = "1984",
title = "Some Simple Estimates for Singular Values of a Matrix",
journal = "Linear Algebra and Its Applications",
volume = "56",
pages = "105-119",
kwds = "svd, pert, Gerschgorin's theorem"
}
-qj- -qk- -ql- -qm- -qn- -qo- -qp- -qq- -qr-
-qs- -qt- -qu- -qv- -qw- -qx- -qy- -qz-
-ra-
@article{rast:88,
author = "C.M. Rader and A.O. Steinhardt",
year = "1988",
title = "Hyperbolic {Householder} transforms",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "9",
pages = "269--290",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, updating, Householder transformation,
hyperbolic transformation"
}
@book{rain:57,
author = "H. F. Rainsford",
year = "1957",
title = "Survey Adjustments and Least Squares",
publisher = "Constable and Company",
address = "London",
kwds = "book, stat, lsq, geodesy"
}
@article{rawe:77,
author = "H. Ramsin and P.-{\AA}. Wedin",
year = "1977",
title = "A Comparison of Some Algorithms for the Nonlinear
Least Squares Problem",
journal = "BIT",
volume = "17",
pages = "72--90",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@book{rami:71,
author = "C. R. Rao and S. K. Mitra",
year = "1971",
title = "Generalized Inverse of Matrices and Its Applications",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, ginv"
}
@book{rao:73,
author = "C. R. Rao",
year = "1973",
title = "Linear Statistical Inference and Its Applications",
edition = "2nd",
publisher = "John Wiley",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "book, stat, regr"
}
@incollection{rao:80,
author = "C. R. Rao",
year = "1980",
title = "Matrix Approximations and Reduction of Dimensionality in
Multivariate Statistical Analysis",
booktitle = "Multivariate Analysis--V",
editor = "P. R. Krishnaiah",
publisher = "North-Holland",
address = "Amsterdam",
kwds = "stat, la, svd, gsvd, matrix approximation, multivariate analysis,
Procrustes problem"
}
@article{rao:81,
author = "C. R. Rao",
year = "1981",
title = "A Lemma on G-Inverse of a Matrix and Computation of Correlation
Coeffiecients in the Singular Case",
journal = "Communications in Statistics (A)",
volume = "10",
pages = "1-10",
kwds = "stat, ginv, correlation, singular system"
}
@article{rath:82,
author = "W. Rath",
year = "1982",
title = "Fast {G}ivens Rotations for Orthogonal Similarity",
journal = "Numerische Mathematik",
volume = "40",
pages = "47--56",
note = "Cited in \cite{govl:89}.",
kwds = "nla, plane rotation, fast algorithm, eig"
}
@article{rayl:1899,
author = "Lord {Rayleigh (J. W. Strutt)}",
year = "1899",
title = "On the Calculation of the Frequency of Vibration of
a System in its Gravest Mode, with an Example from
Hydrodynamics",
journal = "The Philosophical Magazine",
volume = "47",
pages = "556--572",
note = "Cited in \cite{parl:80}",
kwds = "la, eig, Rayleigh quotient, Rayleigh-Ritz method, pert"
}
-rb- -rc- -rd- -re-
@article{rewa:84,
author = "R. A. Redner and H. F. Walker",
year = "1984",
title = "Mixture Densities, Maximum Likelihood and the
{EM}~Algorithm",
journal = "SIAM Review",
volume = "26",
pages = "195--239",
kwds = "stat, nlop, EM algorithm"
}
@article{regr:90,
author = "L. Reichel and W. B. Gragg",
year = "1990",
title = "Algorithm 686: {FORTRAN} subroutines for updating
the {QR} decomposition",
journal = "ACM Transactions on Mathematical Software",
volume = "16",
pages = "369--377",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, updating, software, qrd, Gram-Schmidt algorithm"
}
@article{reid:67,
author = "J. K. Reid",
year = "1967",
title = "A Note on the Least Squares Solution of a Band System of
Linear Equations by {Householder} Reductions",
journal = "Comput Journal",
volume = "10",
pages = "188--189",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, band matrix, Householder transformation, qrd, lsq"
}
@proceedings{reid:71,
editor = "J. K. Reid",
year = "1971",
title = "Large Sparse Sets of Linear Equations",
publisher = "Academic Press",
address = "New York",
kwds = "math, nla, lud, sparse, linear system"
}
@article{reid:71a,
author = "J. K. Reid",
year = "1971",
title = "A Note on the Stability of {Gaussian} Elimination",
journal = "J. Inst. Maths Applics",
volume = "8",
pages = "374--375",
kwds = "la, lud, rounding error"
}
@inproceedings{reid:71b,
author = "J. K. Reid",
year = "1971",
title = "On the Method of Conjugate Gradients for the Solution
of Large Sparse Systems of Linear Equations",
booktitle = "Large Sparse Sets of Linear Equations",
editor = "J. K. Reid",
pages = "231--254",
publisher = "Academic Press",
address = "New York",
kwds = "nla, conjugate gradients, sparse, linear system"
}
@article{reid:72,
author = "J. K. Reid",
year = "1972",
title = "The Use of Conjugate Gradients for Systems of Linear
Equations Possessing ``Property~{A}''",
journal = "SIAM Journal on Numerical Analysis",
volume = "9",
pages = "325--332",
kwds = "nla, conjugate gradients, sparse"
}
@article{reid:74,
author = "J. K. Reid",
year = "1974",
title = "Monitoring the Stability of the Triangular Factorization
of a Sparse Matrix",
journal = "Numerische Mathematik",
volume = "22",
pages = "183--186",
kwds = "nla, lud, sparse"
}
@article{reie:50,
author = "O. Reiers{\o}l",
year = "1950",
title = "Identifiability of a Linear Relation Between Variables
which are Subject to Error",
journal = "Econometrica",
volume = "18",
pages = "375--389",
kwds = "stat, regr, eriv"
}
@article{reba:68,
author = "C. Reinsch and F. L. Bauer",
year = "1968",
title = "Rational {QR}~Transformation with Newton Shift
for Symmetric Tridiagonal Matrices",
journal = "Numerische Mathematik",
volume = "11",
pages = "264--272",
note = "Also in \cite[pp.257--272]{wire:71}.",
kwds = "nla, eig, symmetric matrix, tridiagonal Matrix, QR algorithm,
software"
}
-rf- -rg- -rh-
@article{rhei:68,
author = "W. C. Rheinboldt",
year = "1968",
title = "A Unified Convergence Theory for a Class of
Iterative Processes",
journal = "SIAM Journal on Numerical Analysis",
volume = "5",
pages = "42--63",
kwds = "nlop"
}
@article{rhva:73,
author = "W. C. Rheinboldt and J. S. Vandergraft",
year = "1973",
title = "A Simple Approach to the {Perron--Frobenius} Theory
for Positive Operators on General Partially-Ordered
Finite-Dimensional Linear Spaces",
journal = "Mathematics of Computation",
volume = "27",
pages = "139--145",
kwds = "la, eig, nonnegative matrix"
}
@article{rhme:73,
author = "W. C. Rheinboldt and C. K. mesztenyi",
year = "1973",
title = "Arc Graphs and Their Possible Application to Sparse
Matrix Problems",
journal = "BIT",
volume = "14",
pages = "227--239",
kwds = "nla, sparse, linear system, graph"
}
@article{rhva:74,
author = "W. C. Rheinboldt and J. S. Vandergraft",
year = "1974",
title = "On the Local Convergence of Update Methods",
journal = "SIAM Journal on Numerical Analysis",
volume = "11",
pages = "1069--1085",
kwds = "nlop, quasi-Newton"
}
@article{rhme:74,
author = "W. C. Rheinboldt and C. K. Mesztenyi",
year = "1974",
title = "Arc Graphs and Their Possible Application to
Sparse Matrix Problems",
journal = "BIT",
volume = "14",
pages = "227--239",
kwds = "nla, lud, sparse"
}
-ri-
@article{rice:66,
author = "J. R. Rice",
year = "1966",
title = "Experiments on {Gram--Schmidt} Orthogonalization",
journal = "Mathematics of Computation",
volume = "20",
pages = "325--328",
kwds = "nla, rounding error, Gram-Schmidt algorithm"
}
@article{rice:66a,
author = "J. R. Rice",
year = "1966",
title = "A Theory of Condition",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "3",
pages = "287--310",
note = "Cited in \cite{govl:89}.",
kwds = "na, condition, pert"
}
@book{rice:81,
author = "J. R. Rice",
year = "1981",
title = "Matrix Computations and Mathematical Software",
publisher = "McGraw-Hill",
address = "New York",
kwds = "book, cs, software"
}
@article{rich:73,
author = "W. R. Richert",
year = "1973",
title = "{Eine Fehlerabsch\"atzung f\"ur Eigenwertaufgaben vom
Typ $(\lambda^2I-\lambda A - B)x = 0$}",
journal = "{Zeitschrift f\"ur Angewandte Mathematik und Mechanik}",
volume = "53",
pages = "",
kwds = "nla, geig, pert"
}
@inproceedings{rieg:81,
author = "C. Rieger",
year = "1981",
title = "{ZMOB}: Hardware from a User's Viewpoint",
booktitle = "Proceedings of the IEEE Computer Society
Conference on Pettern Recognition and
Image Processing",
pages = "399-408",
kwds = "cs, prll, architecture, message passing, zmob"
}
@book{ries:55,
author = "F. Riesz and B. Sz.-Nagy",
year = "1955",
title = "Functional Analysis",
publisher = "Ungar",
address = "New York",
note = "L. F. Boron, Translator.",
kwds = "book, math, functional analysis"
}
@article{riga:67,
author = "J. L. Rigal and J. Gaches",
year = "1967",
title = "On the Compatibility of a Given Solution with the Data
of a Linear System",
journal = "Journal of the ACM",
volume = "14",
pages = "543--548",
kwds = "la, nla, pert, backward perturbation"
}
@article{rine:55,
author = "R. F. Rinehart",
year = "1955",
title = "The Equivalence of Definitions of a Matrix Function",
journal = "American Mathematical Monthly",
volume = "62",
pages = "395--414",
note = "Cited in \cite{govl:89}.",
kwds = "na, matrix function"
}
@article{riss:73,
author = "J. Rissanen",
year = "1973",
title = "Algorithms for Triangular Decomposition of Block {H}ankel and
{T}oeplitz Matrices with Application to Factoring Positive Matrix
Polynomials",
journal = "Mathematics of Computation",
volume = "27",
pages = "147--154",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, block algorithm, block Hankel matrix,
block Toeplitz matrix, matrix polynomial"
}
@article{ritz:09,
author = "W. Ritz",
year = "1909",
title = " {\"Uber eine neue Method zur L\"osung gewisser
Variationsprobleme der mathematischen Physik}",
journal = " {Journal f\"ur die reine und angewandte Mathematik}",
volume = "135",
pages = "1--61",
kwds = "la, eig, pert, Rayleigh-Ritz method"
}
-rj- -rk- -rl- -rm- -rn- -ro-
@book{robe:90,
author = "Y. Robert",
year = "1990",
title = "The Impact of Vector and Parallel Architectures on the
Gaussian Elimination Algorithm",
publisher = "Halsted Press",
address = "New York",
kwds = "book, nla, lud, prll, vect, systolic"
}
@article{robe:77,
author = "H. H. Robertson",
year = "1977",
title = "The Accuracy of Error Estimates for Systems of Linear Algebraic
Equations",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "20",
pages = "409--414",
note = "Cited in \cite{govl:89}.",
kwds = "nla, rounding error, linear system"
}
@article{robi:80,
author = "D. W. Robinson",
year = "1980",
title = "Gauss and Generalized Inverses",
journal = "Historia Mathematica",
volume = "7",
pages = "118-125",
kwds = "math, la, Gauss, ginv, history"
}
@article{rodr:73,
author = "G. Rodrigue",
year = "1973",
title = "A Gradient Method for the Matrix Eigenvalue Problem
{$Ax = \lambda Bx$}",
journal = "Numerische Mathematik",
volume = "22",
pages = "1--16",
kwds = "nla, geig, sparse"
}
@book{rode:82a,
editor = "G. Roderigue",
year = "1982",
title = "Parallel Computations",
publisher = "Academic Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "book, na, prll"
}
@article{rowo:84,
author = "G. Roderigue and D. Wolitzer",
year = "1984",
title = "Preconditioning by Incomplete Block Cyclic Reduction",
journal = "Mathematics of Computation",
volume = "42",
pages = "549--566",
note = "Cited in \cite{govl:89}.",
kwds = "nla, preconditioning, block algorithm, cyclic reduction,
incomplete factorization"
}
@article{rohr:31,
author = "H. Rohrbach",
year = "1931",
title = " {Bemerkungen zu einem Determinantensatz von Minkowski}",
journal = "Jahresbericht der Deutschen Mathematiker Vereinigung",
volume = "40",
pages = "49--53",
kwds = "la, pert, eig, Gerschgorin's theorem, determinant"
}
@article{roor:88,
author = "C. H. Romine and J. M. Ortega",
year = "1988",
title = "Parallel Solution of Triangular Systems of Equations",
journal = "Parallel ",
volume = "6",
pages = "109--114",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, triangular matrix, linear system"
}
@article{rose:69,
author = "D. J. Rose",
year = "1969",
title = "An Algorithm for Solving a Special Class of Tridiagonal Systems of
Linear Equations",
journal = "Communications of the {ACM}",
volume = "12",
pages = "234--236",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, tridiagonal matrix"
}
@article{rose:70,
author = "D. J. Rose",
year = "1970",
title = "Triangulated Graphs and the Elimination Process",
journal = "Mathematical Analysis and Applications",
volume = "32",
pages = "597--609",
kwds = "nla, lud, sparse"
}
@article{rose:71,
author = "D. J. Rose",
year = "1971",
title = "A Note on Consistent Ordering and Zero Circulation",
journal = "Journal of the ACM",
volume = "18",
pages = "573--575",
kwds = "nla, iter, sparse"
}
@inproceedings{rose:72,
author = "D. J. Rose",
year = "1972",
title = "A Graph-Theoretic Study of the Numerical Solution
of Sparse Positive Definite Systems of Linear Equations",
booktitle = "Graph Theory and Computing",
editor = "R. C. Read",
pages = "",
publisher = "Academic Press",
address = "New York",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, complexity"
}
@proceedings{rowi:72,
editor = "D. J. Rose and R. A. Willoughby",
year = "1972",
title = "Sparse Matrices and Their Applications",
publisher = "Plenum Press",
address = "New York",
kwds = "math, nla, sparse"
}
@incollection{robu:72,
author = "D. J. Rose and J. R. Bunch",
year = "1972",
title = "The Role of Partitioning in the Numerical Solution
of Sparse Systems",
booktitle = "Sparse Matrices and Their Applications",
editor = "D. J. Rose and R. A. Willoughby",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, sparse, lud"
}
@article{rose:84,
author = "D. J. Rose",
year = "1984",
title = "Convergent Regular Splittings for Singular {M}-Matrices",
journal = "SIAM Journal on Algebraic and Discrete Methods",
volume = "5",
pages = "133-144",
kwds = "nla, Markov chain, M-matrix, singular system"
}
@article{rose:60,
author = "J. B. Rosen",
year = "1960",
title = "The Gradient Projection Method for Nonlinear Programming.
Part {I}. Linear Constraints",
journal = "SIAM Journal",
volume = "8",
pages = "181--217",
kwds = "nlop"
}
@article{rose:61,
author = "J. B. Rosen",
year = "1961",
title = "The Gradient Projection Method for Nonlinear Programming.
Part {II}. Nonlinear Constraints",
journal = "SIAM Journal",
volume = "9",
pages = "514--532",
kwds = "nlop"
}
@article{rose:56,
author = "M. Rosenblum",
year = "1956",
title = "On the Operator Equation {$BX-XA = Q$}",
journal = "Duke Mathematical Journal",
volume = "23",
pages = "263--269",
kwds = "la, eig, Sylvester equation, pert, matrix equation"
}
@article{roth:81,
author = "U. Rothblum",
year = "1981",
title = "Resolvent Expansions of Matrices and Applications",
journal = "Linear Algebra and Its Applications",
volume = "38",
pages = "33--49",
kwds = "la, resolvent matrix"
}
@article{rosa:78,
author = "P. Rousseau and D. Sankoff",
year = "1978",
title = "Singularities in the Analysis of Binomial Data",
journal = "Biometrika",
volume = "65",
pages = "603--608",
kwds = "stat, categorical data"
}
@inproceedings{roka:90,
author = "R. Roy and T. Kailath",
year = "1990",
title = "{ESPRIT}--Estimation of Signal Parameters Via
Rotational Invariance Techniques",
booktitle = "Signal Processing Part {II}: Control Theory and Applications",
editor = "F. A. Gr{\"u}nbaum and J. W. Helton and P. Khargonekar",
pages = "369--411",
publisher = "Springer",
address = "New York",
kwds = "signal processing, direction of arrival"
}
-rp- -rq- -rr- -rs- -rt- -ru-
@article{ruhe:68,
author = "A. Ruhe",
year = "1968",
title = "On the Quadratic Convergence of a Generalization of
the {Jacobi} Method to Arbitrary Matrices",
journal = "BIT",
volume = "8",
pages = "210--231",
kwds = "nla, eig, Jacobi-like, nonsymmetric matrix"
}
@article{ruhe:69,
author = "A. Ruhe",
year = "1969",
title = "The Norm of a Matrix After a Similarity Transformation",
journal = "BIT",
volume = "9",
pages = "53-58",
kwds = "la, eig, norm, pert"
}
@article{ruhe:69a,
author = "A. Ruhe",
year = "1969",
title = "An Algorithm for Numerical Determination of the Structure of a
General Matrix",
journal = "{BIT}",
volume = "10",
pages = "196--216",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig"
}
@article{ruhe:70,
author = "A. Ruhe",
year = "1970",
title = "Perturbation Bounds for Means of Eigenvalues and
Invariant Subspaces",
journal = "BIT",
volume = "10",
pages = "343--354",
kwds = "la, eig, pert, invariant subspace"
}
@article{ruhe:70a,
author = "A. Ruhe",
year = "1970",
title = "An Algorithm for Numerical Determination of the Structure
of a General Matrix",
journal = "BIT",
volume = "10",
pages = "196--216",
kwds = "nla, eig"
}
@article{ruhe:70b,
author = "A. Ruhe",
year = "1970",
title = "Properties of a Matrix with a Very Ill-Conditioned Eigenproblem",
journal = "Numerische Mathematik",
volume = "15",
pages = "57--60",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, pert, ill-conditioned problem, condition"
}
@article{ruwi:72,
author = "A. Ruhe and T. Wiberg",
year = "1972",
title = "The Method of Conjugate Gradients Used in Inverse
Iteration",
journal = "BIT",
volume = "12",
pages = "543--554",
kwds = "nla, sparse, conjugate gradients, eig, inverse iteration"
}
@article{ruhe:74,
author = "A. Ruhe",
year = "1974",
title = "{SOR}-Methods for the Eigenvalue Problem with Large
Sparse Matrices",
journal = "Mathematics of Computation",
volume = "28",
pages = "695--710",
kwds = "nla, eig, sparse, relaxation"
}
@article{ruhe:75,
author = "A. Ruhe",
year = "1975",
title = "On the Closeness of Eigenvalues and Singular Values for Almost
Normal Matrices",
journal = "Linear Algebra and its Applications",
volume = "11",
pages = "87--94",
note = "Cited in \cite{govl:89}.",
kwds = "la, eig, svd, normal matrix, pert"
}
@article{ruhe:78,
author = "A. Ruhe",
year = "1978",
title = "A Note on the Efficient Solution of Matrix Pencil Systems",
journal = "{BIT}",
volume = "18",
pages = "276--281",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig"
}
@article{ruhe:79,
author = "A. Ruhe",
year = "1979",
title = "Accelerated {Gauss-Newton} Algorithms for Nonlinear Least
Squares Problems",
journal = "BIT",
volume = "19",
pages = "356--367",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Gauss-Newton method"
}
@article{ruhe:79a,
author = "A. Ruhe",
year = "1979",
title = "Implementation Aspects of Band {L}anczos Algorithms for Computation
of Eigenvalues of Large Sparse Symmetric Matrices",
journal = "Mathematics of Computation",
volume = "33",
pages = "680--687",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm, band matrix, sparse"
}
@article{ruhe:80,
author = "A. Ruhe",
year = "1980",
title = "The Relation Between the {Jacobi} Algorithm and Inverse
Iteration and a {Jacobi} Algorithm Based on Elementary
Refelctions",
journal = "BIT",
volume = "20",
pages = "88--96",
kwds = "nla, eig, Jacobi's method, inverse iteration"
}
@article{ruwe:80,
author = "A. Ruhe and P.-{\AA}. Wedin",
year = "1980",
title = "Algorithms for Separable Nonlinear Least Squares Problems",
journal = "SIAM Review",
volume = "22",
pages = "318--337",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@article{ruhe:83,
author = "A. Ruhe",
year = "1983",
title = "Numerical Aspects of {Gram--Schmidt} Orthogonalization
of Vectors",
journal = "Linear Algebra and Its Applications",
volume = "53/53",
pages = "591--601",
kwds = "nla, qrd, Gram-Schmidt algorithm"
}
@article{ruhe:87,
author = "A. Ruhe",
year = "1987",
title = "Closest Normal Matrix Finally Found",
journal = "BIT",
volume = "27",
pages = "585--598",
kwds = "la, pert, normal matrix, matrix approximation"
}
@article{rung:1884,
author = "C. Runge",
year = "1884",
title = "{Entwicklung der Wurzeln einer Algebraischen Gleichung
in Summen von rationalen Functionen der Coefficienten}",
journal = "Acta Mathematica",
volume = "6",
pages = "305--318",
kwds = "nlop, polynomial"
}
@article{rubs:66,
author = "B. Rust and W. R. Burrus and C. Schneeberger",
year = "1966",
title = "A Simple Algorithm for Computing the Generalized
Inverse of a Matrix",
journal = "Communications of the ACM",
volume = "9",
pages = "331--386",
kwds = "nla, ginv"
}
@article{ruti:53,
author = "H. Rutishauser",
year = "1953",
title = "{Beitr\"age zur Kenntnis des Biorthogonalisierungs-Algorithmus
von Lanczos}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "4",
pages = "35--56",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix, sparse"
}
@article{ruti:54,
author = "H. Rutishauser",
year = "1954",
title = "{Der Quotienten-Differenzen-Algorithmus}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "5",
pages = "233--251",
kwds = "nlop, polynomial, qd-algorithm"
}
@article{ruti:54a,
author = "H. Rutishauser",
year = "1954",
title = "{Anwendungen Des Quotienten-Differenzen-Algorithmus}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "5",
pages = "496--508",
kwds = "nlop, polynomial, qd-algorithm"
}
@article{ruti:55,
author = "H. Rutishauser",
year = "1955",
title = "Une m\'ethode pour la d\/etermination des valeurs
propres d'une matrice",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "240",
pages = "34-36",
kwds = "nla, eig, LR algorithm"
}
@article{ruba:??,
author = "H. Rutishauser and F. L. Bauer",
year = "19??",
title = "{D\'etermination des vecteurs propres d'une matrice
par une m\'ethode it\'erative avec convergence
quadratique}",
journal = "Comptes Rendus de l'Acad\'emie des Sciences, Paris",
volume = "???",
pages = "1680--1681",
kwds = "nla, eig"
}
@article{ruti:56,
author = "H. Rutishauser",
year = "1956",
title = "{Eine Formel von Wronski und ihre Bedeutung f\"ur den
Quotienten-Differenzen-Algorithmus}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "7",
pages = "164--169",
kwds = "nlop, polynomial, qd-algorithm"
}
@article{ruti:58,
author = "H. Rutishauser",
year = "1958",
title = "Solution of Eigenvalue Problems with the {LR}-Transformation",
journal = "National Bureau of Standards Applied Mathematics Series",
volume = "49",
pages = "47--81",
kwds = "nla, eig, LR algorithm"
}
@article{ruti:59,
author = "H. Rutishauser",
year = "1959",
title = "{Deflation bei Bandmatrizen}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und Physik}",
volume = "10",
pages = "314--319",
kwds = "nla, eig, band matrix, symmetric matrix"
}
@article{ruti:66,
author = "H. Rutishauser",
year = "1966",
title = "The {Jacobi} Method for Real Symmetric Matrices",
journal = "Numerisch Mathematik",
volume = "9",
pages = "1-10",
note = "Also in \cite[pp.202--211]{wire:71}.",
kwds = "math, nla, eig, symmetric matrix, Jacobi's method, software"
}
@article{ruti:69,
author = "H. Rutishauser",
year = "1969",
title = "Computational Aspects of {F. L. Bauer's} Simultaneous
Iteration Method",
journal = "Numerische Mathematik",
volume = "13",
pages = "4--13",
kwds = "nla, eig, subspace iteration, sparse, symmetric matrix"
}
@article{ruti:70,
author = "H. Rutishauser",
year = "1970",
title = "Simultaneous Iteration Method for Symmetric Matrices",
journal = "Numerische Mathematik",
volume = "16",
pages = "205--223",
note = "Also in \cite[pp.284--301]{wire:71}.",
kwds = "nla, eig, subspace iteration, symmetric matrix, sparse,
software"
}
-rv- -rw- -rx- -ry- -rz-
-sa-
@article{saad:80,
author = "Y. Saad",
year = "1980",
title = "Variations of {Arnoldi's} Method for Computing Eigenelements
of Large Unsymmetric Matrices",
journal = "Linear Algebra and Its Applications",
volume = "34",
pages = "269--295",
kwds = "nla, eig, Arnoldi's method, nonsymmetric matrix"
}
@article{saad:80a,
author = "Y. Saad",
year = "1980",
title = "On the Rates of Convergence of the {L}anczos
and the Block {L}anczos Methods",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "17",
pages = "687--706",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, block algorithm"
}
@article{saad:81,
author = "Y. Saad",
year = "1981",
title = "{K}rylov Subspace Methods for Solving Large Unsymmetric Linear
Systems",
journal = "Mathematics of Computation",
volume = "37",
pages = "105--126",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, nonsymmetric matrix, Krylov sequence"
}
@inproceedings{saad:83b,
author = "Y. Saad",
year = "1983",
title = "Projection Methods for Solving Large Sparse Eigenvalue Problems",
booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
pages = "121--144",
publisher = "Springer",
address = "New York",
kwds = "nla, eig, nonsymmetric matrix, Arnoldi's method"
}
@techreport{saad:83,
author = "Y. Saad",
year = "1983",
title = "Least Squares Polynomials in the Complex Plane
with Applications to Solving Sparse Nonsymmetric
Matrix Problems",
institution = "Department of Computer Science, Yale Univerisity",
type = "Research Report",
number = "RR--276",
kwds = "nla, eig, linear system, sparse, nonsymmetric matrix"
}
@techreport{saad:83a,
author = "Y. Saad",
year = "1983",
title = "Practical Use of Polynomial Preconditionings for
the Conjugate Gradient Method",
institution = "Department of Computer Science, Yale Univerisity",
type = "Research Report",
number = "RR--282",
kwds = "nla, conjugate gradients, preconditioning"
}
@techreport{sash:83,
author = "Y. Saad and M. H. Schultz",
year = "1983",
title = "Conjugate Gradient-Like Algorithms for Solving
Nonsymmetric Linear Systems",
institution = "Department of Computer Science, Yale Univerisity",
type = "Research Report",
number = "RR--283",
kwds = "nla, conjugate gradients, nonsymmetric matrix"
}
@article{saad:84,
author = "Y. Saad",
year = "1984",
title = "Chebyshev Acceleration Techniques for Solving
Nonsymmetric Eigenvalue Problems",
journal = "Mathematics of Computation",
volume = "42",
pages = "567-588",
kwds = "nla, eig, sparse, Chebyshev acceleration, nonsymmetric matrix"
}
@article{saad:84a,
author = "Y. Saad",
year = "1984",
title = "Practical Use of Some {K}rylov Subspace Methods for Solving
Indefinite and Nonsymmetric Linear Systems",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "5",
pages = "203--228",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, nonsymmetric matrix, indefinite system,
Krylov sequence"
}
@techreport{sasc:85,
author = "Y. Saad and M. H. Schulz",
year = "1985",
title = "Topological Properties of Hypercubes",
institution = "Department of Computer Science,
Yale University",
type = "Research Report",
number = "YALE/DCS/RR-389",
kwds = "prll, hypercube, communication"
}
@techreport{sasc:85a,
author = " Y. Saad and M. H. Schultz",
year = "1985",
title = "Data Communication in Hypercubes",
number = "YALEU DCS RR-428",
institution = "Computer Science, Yale University",
address = "New Haven, CT",
note = "Cited in \cite{govl:89}.",
kwds = "cs, prll, hypercube, communication"
}
@techreport{saad:85,
author = "Y. Saad",
year = "1985",
title = "Partial Eigensolutions of Large Nonsymmetric Matrices",
institution = "Department of Computer Science, Yale University",
type = "Research Report",
number = "YALEU/DCS/RR-397",
kwds = "nla, eig, sparse, nonsymmetric matrix"
}
@article{saad:86,
author = "Y. Saad",
year = "1986",
title = "On the Condition Number of Some {G}ram Matrices Arising from Least
Squares Approximation in the Complex Plane",
journal = "Numerische Mathematik",
volume = "48",
pages = "337--348",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lsq, condition, Gram matrix"
}
@article{sasc:86,
author = "Y. Saad and M. Schultz",
year = "1986",
title = "{GMRES}: A Generalized Minimal Residual Algorithm for Solving
Nonsymmetric Linear Systems",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "7",
pages = "856--869",
note = "Cited in \cite{govl:89}.",
kwds = "nla, GMRES, linear system"
}
@article{saad:87,
author = "Y. Saad",
year = "1987",
title = "On the {L}anczos Method for Solving Symmetric Systems with Several
Right Hand Sides",
journal = "Mathematics of Computation",
volume = "48",
pages = "651--662",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, linear system"
}
@inproceedings{saad:91,
author = "Y. Saad",
year = "1990",
title = "Projection Methods for the Numerical Solution of
{Markov} Chains",
booktitle = "Nuermical Solution of Markov Chains",
editor = "W. J. Stewart",
pages = "455--472",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, pert, Markov chain, eig"
}
@article{sala:87,
author = "D. E. Salane",
year = "1987",
title = "A Continuation Approach for Solving Large Residual Least
Squares Problems",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "655--671",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, continuation"
}
@mastersthesis{sals:78,
author = "K. Salsburg",
year = "1978",
title = "The Method of Simultaneous Conjugate Gradients",
school = "Applied Mathematics Program, University of Maryland,
College Park",
kwds = "nla, eig, sparse, conjugate gradients, symmetric matrix"
}
@article{same:71,
author = "A. Sameh",
year = "1971",
title = "On {J}acobi and {J}acobi-Like Algorithms for a Parallel Computer",
journal = "Mathematics of Computation",
volume = "25",
pages = "579--590",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, prll, Jacobi's method, Jacobi-like"
}
@article{saln:75,
author = "A. Sameh and J. Lermit and K. Noh",
year = "1975",
title = "On the Intermediate Eigenvalues of Symmetric Sparse Matrices",
journal = "{BIT}",
volume = "12",
pages = "543--554",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, interior eigenvalue, sparse, symmetric matrix"
}
@article{saku:78,
author = "A. Sameh and D. Kuck",
year = "1978",
title = "On Stable Parallel Linear System Solvers",
journal = "Journal of the {ACM}",
volume = "25",
pages = "81--91",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, prll"
}
@article{same:59,
author = "K. Samelson",
year = "1959",
title = "{Faktorisierung von Polynomen durch functionale Iteration}",
journal = "Abhandlungen der Bayerische Akademie der Wissenschaften,
Mathematische-Naturwissenschaftliche Klasse",
volume = "95",
pages = "5--25",
kwds = "nlop, polynomial"
}
@techreport{saun:72,
author = "M. A. Saunders",
year = "1972",
title = "Large-Scale Linear Programming Using The {Cholesky} Factorization",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS252",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Cholesky decomposition, updating, linear programming"
}
-sb- -sc-
@article{scha:85,
author = "R. Schaback",
year = "1985",
title = "Convergence Analysis of the General {Gauss-Newton} Algorithm",
journal = "Numerische Mathematik",
volume = "46",
pages = "281--309",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Gauss-Newton method"
}
@book{sche:59,
author = "H. Scheffe",
year = "1959",
title = "The Analysis of Variance",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, stat, anova, regr"
}
@article{scst:79,
author = "K. Schittkowski and J. Stoer",
year = "1979",
title = "A Factorization Method for the Solution of Constrained
Linear Least Squares Problems Allowing Subsequent
Data Changes",
journal = "Numerische Mathematik",
volume = "31",
pages = "431--463",
kwds = "nla, lsq, qrd, constraints, updating, Gram-Schmidt algorithm"
}
@article{schi:83,
author = "K. Schittkowski",
year = "1983",
title = "The Numerical Solution of Constrained Linear
Least-squares Problems",
journal = "IMA J. Numer. Anal.",
volume = "3",
pages = "11--36",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, constraints"
}
@techreport{schi:85,
author = "K. Schittkowski",
year = "1985",
title = "Solving Constrained Nonlinear Least Squares Problems by a
General Purpose {SOP}-method",
institution = "Institute f{\"u}r Informatik, Universit{\"a}t Stuttgart",
type = "Technical Report",
number = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
@techreport{sczi:85,
author = "K. Schittkowski and P. Zimmerman",
year = "1985",
title = "A Factorization Method for Constrained Least Squares Problems with
Data Changes. Part 2: Numerical Tests, Comparisons, and {ALGOL} Codes",
institution = "Institut f{\"u}r Angewandte Mathematik und Statistik,
Universit{\"a}t, W{\"u}rzburg.",
type = "Preprint",
number = "No.~30",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, qrd, constraints, updating, software, Gram-Schmidt algorithm"
}
@article{schm:07,
author = "E. Schmidt",
year = "1907",
title = "{Zur Theorie der linearen und nichtlinearen Integralgleichungen.
I~Teil. Entwicklung willk\"urlichen Funktionen nach
System vorgeschriebener}",
journal = "Mathematische Annalen",
volume = "63",
pages = "433-476",
kwds = "math, la, qrd, Gram-Schmidt algorithm, svd, matrix approximation,
Schmidt-Mirsky theorem, integral equation"
}
@article{schm:08,
author = "E. Schmidt",
year = "1908",
title = "{\"Uber die Aufl{\"o}sung linearer Gleichungen mit unendlich
vielen Unbekannten}",
journal = "Rendiconti Circolo Matematico du Palermo. Series 1",
volume = "25",
pages = "53--77",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Gram-Schmidt algorithm"
}
@mastersthesis{schm:79,
author = "K. C. Schmidt",
year = "1979",
title = "Selecting Subsets of Variables in the Linear Regression
Problem",
school = "Department of Mathematics, University of Maryland,
College Park",
kwds = "stat, regr, eriv, variable selection"
}
@phdthesis{schm:81,
author = "R. O. Schmidt",
year = "1981",
title = "A signal Subspace Approach to Multiple Emitter Location and
Spectral Estimation",
school = "Stanford University",
kwds = "signal processing, direction of arrival"
}
@article{scpa:84,
author = "R. E. Schnabel and P. D. Frank",
year = "1984",
title = "Tensor Methods for Nonlinear Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "21",
pages = "815--843",
kwds = "nlop"
}
@article{schn:65,
author = "A. J. Schneider",
year = "1965",
title = "Construction of Matrices Having Certain Sign Patterns
and Prescribed Eigenvalues by Orthogonal Transformations",
journal = "IEEE Transactions on Circuit Theory",
volume = "12",
pages = "420--421",
kwds = "nla, test matrix"
}
@article{schn:66,
author = "A. J. Schneider",
year = "1966",
title = "{RC}~Driving-Point Impedance Realization by Linear
Transfromations",
journal = "IEEE Transactions on Circuit Theory",
volume = "13",
pages = "265--271",
kwds = "nla, test matrix"
}
@book{scho:87,
author = "W. Sch{\"o}nauer",
year = "1987",
title = "Scientific Computing on Vector Computers",
publisher = "North-Holland",
address = "Amsterdam",
note = "Cited in \cite{govl:89}.",
kwds = "book, na, vect"
}
@article{scho:61,
author = "A. Sch{\"o}nhage",
year = "1961",
title = "{Zur Konvergenz des Jacobi-Verfahrens}",
journal = "Numerische Mathematik",
volume = "3",
pages = "374--380",
kwds = "nla, Jacobi's method, eig, symmetric matrix"
}
@article{scho:73,
author = "A. Sch{\"o}nhage",
year = "1973",
title = "{Unit\"are Transformationen gro{\ss}er Matrizen}",
journal = "Numerische Mathematik",
volume = "20",
pages = "409--417",
kwds = "nla, qrd, fast algorithm"
}
@article{scho:66,
author = "P. H. Sch{\"o}neman",
year = "1966",
title = "A Generalized Solution of the Orthogonal {Procrustes}
Problem",
journal = "Psychometrika",
volume = "31",
pages = "1--10",
kwds = "la, matrix approximation, svd, Procrustes problem"
}
@article{schr:86,
author = "R. Schreiber",
year = "1986",
title = "Implementation of Adaptive Array Algorithms",
journal = "IEEE Transactions on Acoustics, Speech, and
Signal Processing",
volume = "34",
pages = "1038--1045",
kwds = "nla, updating, eig, qrd, Cholesky decomposition"
}
@article{schr:86,
author = "R. Schreiber",
year = "1986",
title = "Solving Eigenvalue and Singular Value Problems on an Undersized
Systolic Array",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "7",
pages = "441--451",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, svd, systolic"
}
@article{scta:86,
author = "R. Schreiber and W. P. Tang",
year = "1986",
title = "On Systolic Arrays for Updating the {C}holesky Factorization",
journal = "{BIT}",
volume = "26",
pages = "451--466",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Cholesky decomposition, systolic"
}
@article{scpa:87,
author = "R. Schreiber and B. N. Parlett",
year = "1987",
title = "Block Reflectors: Theory and Computation",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "25",
pages = "189--205",
note = "Cited in \cite{govl:89}.",
kwds = "math, la, nla, Householder transformation, qrd, prll"
}
@techreport{schr:87,
author = "Robert Schreiber",
year = "1987",
title = "Systolic Linear Algebra Machines: A Survey",
institution = "Department of Computer Science, Rensselaer
Polytechnic Institute",
type = "Technical Report",
number = "87-18",
kwds = "nla, prll, systolic"
}
@article{scvl:89,
author = "R. Schreiber and Van Loan, C. F.",
year = "1989",
title = "A Storage Efficient {WY} Representation for Products of
{Householder} Transformations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "10",
pages = "53--57",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, block algorithm, prll, Householder transformation"
}
@article{schr:1870,
author = "E. Schr{\"o}der",
year = "1870",
title = "{\"Uber unendliche viele Algorithmen zur Aufl\"osung
der Gleichungen}",
journal = "Mathematische Annalen",
volume = "2",
pages = "317--365",
kwds = "nlop, polynomial"
}
@article{schu:09,
author = "J. Schur",
year = "1909",
title = "{\"Uber die charakteristischen W\"urzeln
einer linearen Substitution mit einer Anwendung
auf die Theorie der Integral\-gleich\-ungen}",
journal = "{Mathematische Annalen}",
volume = "66",
pages = "448-510",
annote = "The first appearance of the Schur form.",
kwds = "la, eig, Schur form"
}
@article{schu:17,
author = "J. Schur",
year = "1917",
title = "{\"Uber Potenzreihen, die im Innern des Einkeitskreise
besch\"ankt sind}",
journal = "{Journal f\"ur die reine und angewandte Mathematik}",
volume = "147",
pages = "205-232",
kwds = "la"
}
@article{schu:21,
author = "J. Schur",
year = "1921",
title = "{\"Uber algebraische Gleichungen, die nur Wurzeln mit
negativen Realteilen besitzen}",
journal = "{Zeitschrift f\"ur Angewandte Mathematik und Mechanik}",
volume = "1",
pages = "307--311",
kwds = "nlop, eig, polynomial"
}
@article{schw:68,
author = "H. R. Schwarz",
year = "1968",
title = "Tridiagonalization of a Symmetric Band Matrix",
journal = "Numerische Mathematik",
volume = "12",
pages = "231--241",
note = "Also in \cite[pp273--283]{wire:71}.",
kwds = "nla, eig, band matrix, tridiagonal matrix, software"
}
@article{schw:74,
author = "H. R. Schwarz",
year = "1974",
title = "The Eigenvalue Problem {$(A-\lambda B)x = 0$} for
Symmetric Matrices of High Order",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "3",
pages = "11-28",
kwds = "nla, geig, symmetric matrix, sparse"
}
@article{schw:74a,
author = "H. R. Schwarz",
year = "1974",
title = "The Method of Coordinate Overrelaxation for
{$(A-\lambda B)x = 0$}",
journal = "Numerische Mathematik",
volume = "23",
pages = "135--151",
kwds = "nla, geig, sparse, relaxation, symmetric matrix"
}
@article{schw:77,
author = "H. R. Schwarz",
year = "1977",
title = "Two Algorithms for Treating {$Ax = \lambda Bx$}",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "12",
pages = "181-199",
kwds = "nla, geig, sparse, symmetric matrix"
}
@article{schwe:68,
author = "P. J. Schweitzer",
year = "1968",
title = "Perturbation Theory and Finite {Markov} Chains",
journal = "Journal of Applied Probability",
volume = "5",
pages = "401-413",
kwds = "la, pert, Markov chain"
}
@techreport{schwe:84,
author = "P. J. Schweitzer",
year = "1984",
title = "The Laurent Expansion for a Nearly Singular Pencil",
institution = "University of Rochester, The Graduate School of Management",
type = "Working Paper",
number = "QM8413",
kwds = "la, geig, Laurent series"
}
@article{scki:86,
author = "P. J. Schweitzer and K. W. Kindle",
year = "1986",
title = "An Iterative Aggregation-Disaggregation Algorithm
for Solving Linear Equations",
journal = "Applied Mathematics and Computation",
volume = "18",
pages = "313--353",
kwds = "nla, linear system, Markov chain, iter, aggregation"
}
@techreport{scst:91,
author = "P. J. Schweitzer and G. W. Stewart",
year = "1991",
title = "The Laurent Expansion of Pencils that are Singular
at the Origin",
institution = "University of Maryland, Department of Computer Science",
type ="Technical Report",
number = "91--164",
note = "To appear in {\it Linear Algebra and Its Applications.\/}",
kwds = "nla, gieg, Laurent expansion, Kronecker form, rank determination"
}
@article{scti:85,
author = "H. Schwetlick and V. Tiller",
year = "1985",
title = "Numerical Methods for Estimating Parameters in Nonlinear Models
with Errors in the Variables",
journal = "Technometrics",
volume = "27",
pages = "17--24",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, eriv"
}
@inproceedings{schw:91,
author = "P. J. Schweitzer",
year = "1990",
title = "A Survey of Aggregation-Disaggregation in Large
{Markov} Chains",
booktitle = "Numerical Methods for {Markov} Chains ",
editor = "W. J. Stewart",
pages = "63--88",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, pert, Markov chain, eig, aggregation"
}
@inproceedings{scol:72,
author = "H. D. Scolnik",
year = "1972",
title = "On the Solution of Non-linear Least Squares Problems",
booktitle = "Proceedings of the {IFIP} Congress 71",
editor = "H. Freeman",
pages = "1258--1265",
publisher = "North-Holland",
address = "Amsterdam",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq"
}
@techreport{scot:78,
author = "D. S. Scott",
year = "1978",
title = "Analysis of the Symmetric {L}anczos Process",
number = "M78/40",
institution = "UCB-ERL, University of California, Berkeley",
address = "Berkeley, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm"
}
@techreport{scot:79,
author = "D. S. Scott",
year = "1979",
title = "Block {L}anczos Software for Symmetric Eigenvalue Problems",
number = "ORNL/CSD-48",
institution = "Oak Ridge National Laboratory",
Address = "Oak Ridge, TN",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos, block algorithm, eig"
}
@article{scot:79a,
author = "D. S. Scott",
year = "1979",
title = "How to Make the {L}anczos Algorithm Converge Slowly",
journal = "Mathematics of Computation",
volume = "33",
pages = "239--247",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm"
}
@article{scba:81,
author = "D. T. Scott and G. R. Bryce and D. M. Allen",
year = "1981",
title = "Orthogonal-Triangularization Methods in Statistical Computations",
journal = "",
volume = "",
pages = "223-244",
kwds = "stat, nla, qrd, regr"
}
@article{scot:84,
author = "D. S. Scott",
year = "1984",
title = "Computing a Few Eigenvalues and Eigenvectors of a Symmetric Band
Matrix",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "5",
pages = "658--666",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, band matrix, symmetric matrix"
}
@article{scot:85,
author = "D. S. Scott",
year = "1985",
title = "On the Accuracy of the {G}ershgorin Circle Theorem for Bounding the
Spread of a Real Symmetric Matrix",
journal = "Linear Algebra and its Applications",
volume = "65",
pages = "147--155",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Gerschgorin's theorem, eig, pert, symmetric matrix"
}
@article{schw:86,
author = "D. S. Scott and M. T. Heath and R. C. Ward",
year = "1986",
title = "Parallel Block {Jacobi} Eigenvalue Algorithms Using
Systolic Arrays",
journal = "Linear Algebra and Its Applications",
volume = "77",
pages = "345-355",
kwds = "nla, prll, eig, systolic, Jacobi's method, symmetric matrix"
}
@incollection{scri:73,
author = "C. J. Scriba",
year = "1973",
title = "{Carl Gustav Jacob Jacobi}",
booktitle = "Dictionary of Scientific Biography, VII",
editor = "C. C. Gillispe",
publisher = "Charles Scribner's Sons",
address = "New York",
kwds = "Jacobi, history"
}
-sd- -se-
@article{seag:86,
author = "M. K. Seager",
year = "1986",
title = "Parallelizing Conjugate Gradient for the {Cray X-MP}",
journal = "Parallel ",
volume = "3",
pages = "35--47",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, prll"
}
@article{seal:67,
author = "H. L. Seal",
year = "1967",
title = "The Historical Development of the {Gauss} Linear Model",
journal = "Biometrika",
volume = "54",
pages = "1-24",
kwds = "stat, Gauss, lsq, regr, history"
}
@book{sear:71,
author = "S.R. Searle",
year = "1971",
title = "Linear Models",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr"
}
@article{sesh:81,
author = "S. R. Searle and F. M. Speed and H. V. Henderson",
year = "1981",
title = "Some Computational and Model Equivalences in Analyses of Variance
of Unequal-Subclass-Numbers Data",
journal = "The American Statistician",
volume = "35",
pages = "16-33",
kwds = "stat, anova"
}
@article{seat:69,
author = "J. J. Seaton",
year = "1969",
title = "Diagonalization of Complex Symmetric Matrices Using a Modified
{J}acobi Method",
journal = "The Computer Journal",
volume = "12",
pages = "156--157",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Jacobi-like, complex matrix, symmetric matrix"
}
@article{seba:41,
author = "Sebasti\~ao e Silva, J.",
year = "1941",
title = "Sur une m\'ethode d'approximation semable \`a celle de
{Gr\"affe}",
journal = "Portugaliae Mathematica",
volume = "2",
pages = "271--279",
kwds = "nlop, polynomial, Graeffe's method, Koenig's theorem"
}
@book{sebe:77,
author = "G. A. F. Seber",
year = "1977",
title = "Linear Regression Analysis",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr"
}
@article{seit:85,
author = "C. Seitz",
year = "1985",
title = "The Cosmic Cube",
journal = "Communications of the ACM",
volume = "28",
pages = "22-33",
kwds = "prll, hypercube, cosmic cube"
}
@article{sebl:79,
author = "S. Serbin and S. Blalock",
year = "1979",
title = "An Algorithm for Computing the Matrix Cosine",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "1",
pages = "198--204",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix cosine"
}
@article{serb:80,
author = "S. Serbin",
year = "1980",
title = "On Factoring a Class of Complex Symmetric Matrices Without
Pivoting",
journal = "Mathematics of Computation",
volume = "35",
pages = "1231--1234",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, complex matrix, symmetric matrix, pivoting"
}
@book{serf:80,
author = "R. J. Serfling",
year = "1980",
title = "Approximation Theorems of Mathematical Statistics",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat"
}
-sf- -sg- -sh-
@article{shaf:78,
author = "Glenn Shafer",
year = "1979",
title = "Non-Additive Probabilities in the Work of
{Bernoulli} and {Lambert}",
journal = "Archive for History of Exact Sciences",
volume = "19",
pages = "309-370",
kwds = "history, Bernoulli, Lambert, probability"
}
@article{shav:70,
author = "I. Shavitt",
year = "1970",
title = "Modification of {Nesbet's} Algorithm for the Iterative
Evaluation of Eigenvalues and Eigenvectors",
journal = "Journal of Computational Physics",
volume = "6",
pages = "124--130",
kwds = "nla, geig, sparse"
}
@article{shav:70a,
author = "I. Shavitt",
year = "1970",
title = "An Iterative Procedure for the Calculation of the
Lowest Real Eigenvalue and Eigenvector of a
Nonsymmetric Matrix",
journal = "Journal of Computational Physics",
volume = "6",
pages = "146--149",
kwds = "nla, geig, sparse, nonsymmetric matrix"
}
@article{sbph:73,
author = "I. Shavitt and C. F. Bender and A. Pipano and R. P. Hosteny",
year = "1973",
title = "The Iterative Calculation of Several of the Lowest or
Highest Eigenvalues and Corresponding Eigenvectors of
Very Large Symmetric Matrices",
journal = "Journal of Computational Physics",
volume = "11",
pages = "90--108",
kwds = "nla, eig, sparse, symmetric matrix"
}
@article{shel:55,
author = "J. W. Sheldon",
year = "1955",
title = "On the Numerical Solution of Elliptic Difference Equations",
journal = "Mathematical Tables and Other Aids to Computation",
volume = "9",
pages = "101--112",
note = "Cited in \cite{govl:89}.",
kwds = "na, pde, elliptic equation"
}
@inproceedings{shmw:87,
author = "T. J. Shepherd and J. G. McWhirter",
year = "1987",
title = "A Pipelined Array for Linearly Constrained Least
Squares Optimization",
booktitle = "Mathematics in Signal Processing",
editor = "T. S. Durrani and J. B. Abbiss and J. E. Hudson and
R. W. Madan and J. G. McWhirter and T. A. Moore",
pages = "607--635",
publisher = "Clarendon Press",
address = "Oxford",
note = "Cited in \cite{mova:91}",
kwds = "nla, lsq, updating, constraints"
}
@article{shey:77a,
author = "O. B. Sheynin",
year = "1977",
title = "{Laplace's} Theory of Errors",
journal = "Archive for History of Exact Sciences",
volume = "17",
pages = "1-61",
kwds = "history, probability, Laplace"
}
@article{shey:77b,
author = "O. B. Sheynin",
year = "1977",
title = "Early History of the Theory of Probability",
journal = "Archive for History of Exact Sciences",
volume = "17",
pages = "201-259",
kwds = "history, probability"
}
@article{shey:79,
author = "O. B. Sheynin",
year = "1979",
title = "{C. F. Gauss} and the Theory of Errors",
journal = "Archive for History of Exact Sciences",
volume = "20",
pages = "21-72",
kwds = "history, probability, Gauss"
}
@article{shst:72,
author = "N. Shinazaki and M. Sibuya and K. Tanabe",
year = "1972",
title = "Numerical Algorithms for the {Moore--Penrose} Inverse
of a Matrix: Direct Methods",
journal = "Annals of the Institute of Statistical Mathematics",
volume = "24",
pages = "193--203",
kwds = "nla, ginv"
}
@article{shst:72a,
author = "N. Shinazaki and M. Sibuya and K. Tanabe",
year = "1972",
title = "Numerical Algorithms for the {Moore--Penrose} Inverse
of a Matrix: Iterative Methods",
journal = "Annals of the Institute of Statistical Mathematics",
volume = "24",
pages = "621--629",
kwds = "nla, ginv, iter"
}
@article{shsh:91,
author = "W. Shougen and Z. Shuqin",
year = "1991",
title = "An Algorithm for {$Ax = \lambda Bx$} with Symmetric
and Positive-Definite {$A$} and {$B$}",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "???--???",
kwds = "nla, geig, symmetric matrix"
}
@article{shra:86,
author = "R. I. Shrager",
year = "1986",
title = "Chemical Transitions Measured by Spectra and Resolved
Using Singular Value Decomposition",
journal = "Chemometrics and Intelligent Laboratory System",
volume = "1",
pages = "59--70",
note = "Reference communicated by the author.",
kwds = "nla, svd, application"
}
@techreport{shsc:87,
author = "G. Shroff and R. Schreiber",
year = "1987",
title = "Convergence of Block {J}acobi Methods",
number = "87-25",
institution = "Computer Science, Rensselaer Polytechnic Institute",
address = "Troy, NY",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, block algorithm"
}
@techreport{shbi:90,
author = "G. M. Shroff and C. H. Bischof",
year = "1990",
title = "Adaptive Condition Estimation for Rank-One Updates
of QR~Factorizations",
institution = "Mathematics and Computer Science Division,
Argonne National Laboratory",
type = "Preprint",
number = "MCS-P166-0790",
kwds = "nla, condition estimation, updating, qrd"
}
-si-
@article{simo:84,
author = "H. Simon",
year = "1984",
title = "Analysis of the Symmetric {L}anczos Algorithm with
Reorthogonalization Methods",
journal = "Linear Algebra and its Applications",
volume = "61",
pages = "101--132",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, Lanczos algorithm, orthogonalization"
}
@article{sian:61,
author = "H. A. Simon and A. Ando",
year = "1961",
title = "Aggregation of Variables in Dynamic Systems",
journal = "Econometrica",
volume = "29",
pages = "111-138",
kwds = "la, nearly uncoupled system, Markov chain, ode, aggregation"
}
@article{simo:62,
author = "H. A. Simon",
year = "1962",
title = "The Architecture of Complexity",
journal = "Proceedings of the American Philosophical Society",
volume = "106",
pages = "467--482",
kwds = "nearly uncoupled systems"
}
@article{sisp:76,
author = "B. Singer and S. Spilerman",
year = "1976",
title = "The Representation of Social Processes by {M}arkov Models",
journal = "American Journal of Sociology",
volume = "82",
pages = "1--54",
note = "Cited in \cite{govl:89}.",
kwds = "eig, Markov chain"
}
@unpublished{siev:91,
author = "L. Sirovich and R. Everson",
year = "1991",
title = "Management and Analysis of Large Scientific
Databases",
note = "Center for Fluid Mechanics, Brown University. Submitted
to {\it The International Journal of Supercomputer
Applications.\/}",
kwds = "nla, svd, data compression"
}
-sj- -sk-
@article{skee:79,
author = "R. D. Skeel",
year = "1979",
title = "Scaling for Numerical Stability in {Gaussian} Elimination",
journal = "Journal of the ACM",
volume = "26",
pages = "494--526",
kwds = "nla, lud, scaling, rounding error"
}
@article{skee:80,
author = "R. D. Skeel",
year = "1980",
title = "Iterative Refinement Implies Numerical Stability for {Gaussian}
Elimination",
journal = "Mathematics of Computation",
volume = "35",
pages = "817--832",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lud, rounding error"
}
@article{skee:81,
author = "R. D. Skeel",
year = "1981",
title = "Effect of Equilibration on Residual Size for Partial Pivoting",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "18",
pages = "449--455",
note = "Cited in \cite{govl:89}.",
kwds = "nla, scaling, rounding error, pivoting, lud"
}
-sl-
@techreport{slei:91,
author = "L. G. Sleijpen",
year = "1991",
title = "Note on the Convergence of the Conjugate Gradient Process",
institution = "Department of Mathematics, Utrecht University",
type = "Prepring",
number = "643",
kwds = "nla, eig, linear system, sparse, conjugate gradients"
}
@techreport{slvd:91,
author = "L. G. Sleijpen and van der Sluis, A.",
year = "1991",
title = "Further Results on the Convergence of CG and Ritz Values",
institution = "Department of Mathematics, Utrecht University",
type = "Prepring",
number = "677",
kwds = "nla, eig, linear system, sparse, conjugate gradients"
}
-sm-
@unpublished{smit:67,
author = "B. T. Smith",
year = "1967",
title = "{ZERPOL}: A Zero Finding Algorithm for Polynomials Using
{Laguerre's} Method",
note = "Manuscript. Department of Computer Science, University
of Toronto",
kwds = "nlop, polynomial, Laguerre's method"
}
@techreport{smit:69,
author = "B. T. Smith",
year = "1969",
title = "Error Bounds, Based upon {Gerschgorin's} Theorems for
the Zeros of a Polynomial",
institution = "Department of Computer Science, University of
Toronto",
type = "Technical Report",
number = "9",
kwds = "nla, nlop, polynomial, Gerschgorin's theorem"
}
@book{sbdg:76,
author = "B. T. Smith and J. M. Boyle and J. J. Dongarra and B. S. Garbow
and Y. Ikebe and V. C. Klema and C. B. Moler",
year = "1976",
title = "Matrix Eigensystem Routines - EISPACK Guide
Lecture Notes in Computer Science",
publisher = "Springer-Verlag",
address = "New York",
edition = "2nd",
kwds = "book, nla, eig, eispack, software"
}
@article{smca:80,
author = "G. Smith and F. Campbell",
year = "1980",
title = "A Critique of Some Ridge Regression Methods",
journal = "Journal of the American Statistical Association",
volume = "75",
pages = "74-81",
kwds = "stat, regr, ridge regression"
}
@article{smit:67a,
author = "R. A. Smith",
year = "1967",
title = "The Condition Numbers of the Matrix Eigenvalue Problem",
journal = "Numerische Mathematik",
volume = "10",
pages = "232--240",
kwds = "la, eig, pert, condition"
}
@article{smit:37,
author = "F. Smithies",
year = "1937",
title = "The Eigen-values and Singular Values of Integral Equations",
journal = "Proceedings of the London Mathematical Society",
volume = "43",
pages = "255-279",
kwds = "na, integral equation, svd"
}
@book{smit:70,
author = "F. Smithies",
year = "1970",
title = "Integral Equations",
publisher = "Cambridge University Press",
address = "Cambridge, England",
note = "Cited in \cite{govl:89}.",
kwds = "book, na, integral equation"
}
-sn-
@article{snza:70,
author = "J. Snyders and M. Zakai",
year = "1970",
title = "On Nonnegative Solutions of the Equation {$AD + DA' = -C$}",
journal = "SIAM Journal on Applied Mathematics",
volume = "18",
pages = "704--714",
kwds = "nla, Lyapunov equation, matrix equation"
}
-so-
@article{sost:74,
author = "T. Soderstrom and G. W. Stewart",
year = "1974",
title = "On the Numerical Properties of an Iteration for
Computing the Moore-Penrose Generalized Inverse",
journal = "SIAM Journal on Numerical Analysis",
volume = "11",
pages = "61--74",
kwds = "nla, ginv, iter"
}
@article{sore:85,
author = "D. C. Sorensen",
year = "1985",
title = "Analysis of Pairwise Pivoting in {Gaussian} Elimination",
journal = "IEEE Transactions on Computers",
volume = "34",
pages = "274--278",
kwds = "nla, lud, pivoting, rounding error"
}
@article{sota:91,
author = "D. C. Sorensen and P. T. P. Tang",
year = "1990",
title = "On the Orthogonality of Eigenvectors Computed by
Divide and Conquer Techniques",
journal = "SIAM Journal on Numerical Analysis",
volume = "28",
pages = "1752--1775",
kwds = "nla, eig, prll, symmetric matrix"
}
-sp-
@article{sphh:78,
author = "F. M. Speed and R. R. Hocking and D. P. Hackney",
year = "1978",
title = "Methods of Analysis of Linear Models with Unbalanced Data",
journal = "Journal of the American Statistical Association",
volume = "73",
pages = "105-112",
kwds = "stat, anova, regr"
}
@article{spre:66,
author = "P. Sprent",
year = "1966",
title = "A Generalized Least-Squares Approach to Linear Functional
Relationships",
journal = "Journal of The Royal Statistical Society, Series B",
volume = "28",
pages = "278-297",
kwds = "stat, regr, lsq, eriv, functional model"
}
@article{spro:78,
author = "D. A. Sprott",
year = "1978",
title = "{Gauss's} Contributions to Statistics",
journal = "Historia Mathematica",
volume = "5",
pages = "183-203",
kwds = "Gauss, history, stat, regr, lsq"
}
-sq- -sr-
@book{srkh:79,
author = "M. S. Srivastava and C. G. Khatri",
year = "1979",
title = "An Introduction to Multivariate Statistics",
publisher = "Elsevier North Holland",
address = "New York",
kwds = "book, stat, multivariate analysis"
}
@article{sriv:70,
author = "V. K. Srivastava",
year = "1970",
title = "On the Expectation of the Inverse of a Matrix",
journal = "Sankhya, Series A",
volume = "32",
pages = "236",
kwds = "la, random matrix, inverse matrix"
}
@article{sriv:72,
author = "V. K. Srivastava",
year = "1972",
title = "Disturbance-Variance Estimation in Simultaneous
Equations when Disturbances are Small",
journal = "Journal of the American Statistical Association",
volume = "67",
pages = "164--168",
kwds = "stat, regr, eriv, pert, simultaneous equations"
}
-ss- -st-
@book{ster:74,
author = "P. H. Sterbenz",
year = "1974",
title = "Floating-Point Computation",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, rounding error, computer arithmetic"
}
@article{stss:89,
author = "G. N. Stenbakken and T. M. Souders and G. W. Stewart",
year = "1989",
title = "Ambiguity Groups and Testability",
journal = "IEEE Transactions on Instrumentation",
volume = "38",
pages = "1989",
kwds = "nla, variable selection"
}
@article{stev:81,
author = "D. Stevenson",
year = "1981",
title = "A Proposed Standard for Binary Floating Point Arithmetic",
journal = "{IEEE} Computer",
volume = "14",
Month = mar,
pages = "51--62",
note = "Cited in \cite{govl:89}.",
kwds = "na, computer arithmetic, rounding error"
}
@article{stew:67,
author = "G. W. Stewart",
year = "1967",
title = "A Modification of Davidon's Minimization Method
to Accept Difference Approximations to Derivatives",
journal = "Journal of the Association for Computing Machinery",
volume = "",
pages = "72--83",
kwds = "nlop, quasi-Newton"
}
@article{67a,
author = "G. W. Stewart",
year = "1967",
title = "A generalization of a theorem of Fan
on Gerschgorin disks",
journal = "Numerische Mathematik",
volume = "10",
pages = "162",
kwds = "la, Gerschgorin's theorem"
}
@article{stew:68,
author = "G. W. Stewart and D. W. Lick",
year = "1968",
title = "The Numerical Treatment of a Thin Plate
Heat Transfer Problem",
journal = "Communications of the Association for Computing
Machinery",
volume = "11",
pages = "639--641",
kwds = "na, pde, relaxation"
}
@article{stew:69,
author = "G. W. Stewart",
year = "1969",
title = "On the Continuity of the Generalized Inverse",
journal = "SIAM Journal on Applied Mathematics",
volume = "17",
pages = "33--45",
kwds = "la, pert, lsq, ginv"
}
@article{stew:69a,
author = "G. W. Stewart",
year = "1969",
title = "Accelerating the Orthogonal Iteration for the Eigenvalues
of a {Hermitian} Matrix",
journal = "Numerische Mathematik",
volume = "13",
pages = "362--376",
kwds = "nla, eig, subspace iteration, symmetric matrix, sparse"
}
@article{stew:69b,
author = "G. W. Stewart",
year = "1969",
title = "Some Iterations for Factoring a Polynomial",
journal = "Numerische Mathematik",
volume = "13",
pages = "458--471",
kwds = "nlop, polynomial"
}
@article{stew:69c,
author = "G. W. Stewart",
year = "1969",
title = "On Lehmer's Method for Finding the Zeros
of a Polynomial",
journal = "Mathematics of Computation",
volume = "23",
pages = "829--836",
kwds = "nlop, polynomial, Lehmer's method"
}
@article{stew:70,
author = "G. W. Stewart",
year = "1970",
title = "Incorporating Origin Shifts into the {QR}~Algorithm for
Symmetric Tridiagonal Matrices",
journal = "Communications of the ACM",
volume = "13",
pages = "365--367",
kwds = "nla, eig, QR algorithm, symmetric matrix, tridiagonal matrix"
}
@article{stew:70a,
author = "G. W. Stewart",
year = "1970a",
title = "Algorithm 384, Eigenvalues and Eigenvectors of a Real
Symmetric Matrix",
journal = "Communications of the ACM",
volume = "13",
pages = "369--371",
note = "Errata p.~750.",
kwds = "nla, eig, QR algorithm, symmetric matrix"
}
@article{stew:70b,
author = "G. W. Stewart",
year = "1970",
title = "On the Convergence of Sebastiao e Silva's Method
for Finding a Zero of a Polynomial",
journal = "SIAM Review",
volume = "12",
pages = "458--460",
kwds = "nlop, polynomial"
}
@article{stew:71,
author = "G. W. Stewart",
year = "1971",
title = "Error Bounds for Approximate Invariant
Subspaces of Closed Linear Operators",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "796-808",
kwds = "la, nla, eig, pert, invariant subspace, functional analysis,
nonsymmetric matrix"
}
@article{stew:71a,
author = "G. W. Stewart",
year = "1971",
title = "Error Analysis of the Algorithm for Shifting the
Zeros of a Polynomial by Synthetic Division",
journal = "Mathematics of Computation",
volume = "25",
pages = "135--139",
kwds = "nlop, polynomial, rounding error"
}
@article{stew:71b,
author = "G. W. Stewart",
year = "1971",
title = "On a Companion Operator for Analytic Functions",
journal = "Numerische Mathematik",
volume = "18",
pages = "26--43",
kwds = "nlop, polynomial, qd-algorithm, subspace iteration"
}
@article{stew:72,
author = "G. W. Stewart",
year = "1972",
title = "On the Sensitivity of the Eigenvalue Problem
{$Ax=\lambda Bx$}",
journal = "SIAM Journal on Numerical Analysis",
volume = "4",
pages = "669--686",
kwds = "la, geig, pert, reducing subspace, nonsymmetric matrix"
}
@article{stew:73,
author = "G. W. Stewart",
year = "1973",
title = "Error and Perturbation Bounds for Subspaces Associated with
Certain Eigenvalue Problems",
journal = "SIAM Review",
volume = "15",
pages = "727-764",
kwds = "math, la, nla, eig, geig, svd, pert, invariant subspace,
reducing subspace"
}
@article{stew:73a,
author = "G. W. Stewart",
year = "1973",
title = "Conjugate Direction Methods for Solving Systems
of Linear Equations",
journal = "Numerische Mathematik",
volume = "21",
pages = "285--297",
kwds = "nla, conjugate gradients, linear system, lud, qrd"
}
@article{stew:73b,
author = "G. W. Stewart",
year = "1973",
title = "Some Iterations for Factoring a Polynomial {II}.
A Generalization of the Secant Method",
journal = "Numerische Mathematik",
volume = "22",
pages = "33--36",
kwds = "nlop, polynomial"
}
@book{stew:73c,
author = "G. W. Stewart",
year = "1973",
title = "Introduction to Matrix Computations",
publisher = "Academic Press",
address = "New York",
kwds = "book, nla"
}
@article{stew:74,
author = "G. W. Stewart",
year = "1974",
title = "Modifying Pivot Elements in Gaussian Elimination",
journal = "Mathematics of Computation",
volume = "28",
pages = "1974",
kwds = "nla, sparse, linear system, lud, pivoting"
}
@inproceedings{stew:74a,
author = "G. W. Stewart",
year = "1974",
title = "The Numerical Treatment of Large Eigenvalue Problems",
booktitle = "Proceedings {IFIP} Congress 74",
publisher = "North-Holland",
pages = "666--672",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, sparse"
}
@article{stew:75,
author = "G. W. Stewart",
year = "1975",
title = "{Gerschgorin} Theory for the Generalized Eigenvalue Problem
{$Ax=\lambda Bx$}",
journal = "Mathematics of Computation",
volume = "29",
pages = "600--606",
kwds = "la, pert, geig, Gerschgorin's theorem"
}
@article{stew:75a,
author = "G. W. Stewart",
year = "1975",
title = "The Convergence of the Method of Conjugate Gradients
at Isolated Extreme Points of the Spectrum",
journal = "Numerische Mathematik",
volume = "24",
pages = "85--93",
kwds = "nla, linear system, conjugate gradients"
}
@incollection{stew:75b,
author = "G. W. Stewart",
year = "1975",
title = "Methods of Simultaneous Iteration for Calculating Eigenvectors of
Matrices",
booktitle = "Topics in Numerical Analysis {II}",
editor = "J. H. Miller",
publisher = "Academic Press",
address = "New York",
pages = "185--196",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, sparse, subspace iteration"
}
@article{stew:76,
author = "G. W. Stewart",
year = "1976",
title = "Simultaneous Iteration for Computing Invariant
Subspaces of a Non-{Hermitian} Matrix",
journal = "{\it Numerische Mathematik\/}",
volume = "25",
pages = "123--136",
kwds = "nla, eig, invariant subspace, subspace iteration, sparse,
nonsymmetric matrix"
}
@article{stew:76a,
author = "G. W. Stewart",
year = "1976",
title = "The Economical Storage of Plane Rotations",
journal = "Numerische Mathematik",
volume = "25",
pages = "137--138",
kwds = "nla, plane rotation"
}
@article{stew:76b,
author = "G. W. Stewart",
year = "1976",
title = "Algorithm 407: {HQR3} and {EXCHNG}: {FORTRAN}
Programs for Calculating
the Eigenvalues of a Real Upper {Hessenberg}
Matrix in a Prescribed Order",
journal = "ACM Transactions on Mathematical Software",
volume = "2",
pages = "275--280",
kwds = "nla, eig, QR algorithm, Hessenberg matrix, software"
}
@incollection{stew:76c,
author = "G. W. Stewart",
year = "1976",
title = "A Bibliographical Tour of the Large Sparse Generalized Eigenvalue
Problem",
booktitle = "Sparse Matrix Computations",
editor = "J. R. Bunch and D. J. Rose",
publisher = "Academic Press",
address = "New York",
pages = "113--130",
kwds = "nla, geig, sparse"
}
@article{stew:76d,
author = "G. W. Stewart",
year = "1976",
title = "The Economical Storage of Plane Rotations",
journal = "Numerische Mathematik",
volume = "25",
pages = "137--138",
note = "Cited in \cite{govl:89}.",
kwds = "nla, plane rotation"
}
@inproceedings{stew:77,
author = "G. W. Stewart",
year = "1977",
title = "Research Development and {LINPACK}",
booktitle = "Mathematical Software III",
editor = "J. R. Rice",
publisher = "Academic Press",
address = "New York",
pages = "1-14",
kwds = "software, nla, linpack, pivoting, backward perturbation, lsq"
}
@article{stew:77a,
author = "G. W. Stewart",
year = "1977",
title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear
Least Squares Problems",
journal = "SIAM Review",
volume = "19",
pages = "634-662",
kwds = "math, la, nla, pert, ginv, projection, lsq"
}
@techreport{stew:77b,
author = "G. W. Stewart",
year = "1977",
title = "Sensitivity Coefficients for the Effects of Errors in the
Independent Variables in a Linear Regression",
institution = "Computer Science Department, University of Maryland",
type = "Technical Report",
number = "TR-571",
kwds = "regr, eriv, pert"
}
@article{stew:77c,
author = "G. W. Stewart",
year = "1977",
title = "Perturbation Bounds for the {QR} Factorization
of a Matrix",
journal = "SIAM Journal on Numerical Analysis",
volume = "1977",
pages = "509--518",
kwds = "la, qrd, pert"
}
@techreport{stew:78,
author = "G. W. Stewart",
year = "1978",
title = "{SRRIT}\,---\,A {FORTRAN} Subroutine to Calculate
the Dominant Invariant Subspaces of a Real Matrix",
institution = "University of Maryland, Department of Computer Science",
type = "Technical Report",
number = "TRR-514",
kwds = "nla, eig, subspace iteration, invariant subspace, software,
nonsymmetric matrix"
}
@incollection{stew:78a,
author = "G. W. Stewart",
year = "1978",
title = "Perturbation Theory for the Generalized Eigenvalue Problem",
booktitle = "Recent Advances in Numerical Analysis",
editor = "de Boor, C. and G. H. Golub",
publisher = "Academic Press",
address = "New York",
pages = "193--206",
kwds = "la, geig, pert"
}
@article{stew:79,
author = "G. W. Stewart",
year = "1979",
title = "The Effects of Rounding Error on an Algorithm for Downdating a
{Cholesky} Factorization",
journal = "Journal of the Institute for Mathematics and Applications",
volume = "23",
pages = "203-213",
kwds = "math, nla, rounding error, updating, Cholesky decomposition, qrd"
}
@article{stew:79a,
author = "G. W. Stewart",
year = "1979",
title = "Perturbation Bounds for the Definite Generalized Eigenvalue
Problem",
journal = "Linear Algebra and Its Application",
volume = "23",
pages = "69-86",
kwds = "math, la, pert, geig, symmetric matrix"
}
@article{stew:79b,
author = "G. W. Stewart",
year = "1979",
title = "A Note on the Perturbation of Singular Values",
journal = "Linear Algebra and Its Applications",
volume = "28",
pages = "213--216",
kwds = "la, svd, pert"
}
@article{stew:80,
author = "G. W. Stewart",
year = "1980",
title = "The Efficient Generation of Random Orthogonal Matrices
with an Application to Condition Estimators",
journal = "SIAM Journal on Numerical Analysis",
volume = "17",
pages = "403--404",
kwds = "la, nla, random matrix, qrd, condition estimation,
orthogonal matrix"
}
@article{stew:80a,
author = "G. W. Stewart",
year = "1980",
title = "The Behavior of a Multiplicity Independent Root-finding
Scheme in the Presence of Rounding Error",
journal = "BIT",
volume = "20",
pages = "526--528",
kwds = "nlop, rounding error, multiple zero"
}
@article{stew:81,
author = "G. W. Stewart",
year = "1981",
title = "On the Implicit Deflation of Nearly Singular
Systems of Linear Equations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "2",
pages = "1981",
kwds = "nla, linear system, condition"
}
@article{stew:81a,
author = "G. W. Stewart",
year = "1981",
title = "Constrained Definite Hessians
Tend to be Well Conditioned",
journal = "Mathematical Programming",
volume = "",
pages = "",
kwds = "nlop, condition, constraints, Hessian"
}
@article{stew:82,
author = "G. W. Stewart",
year = "1982",
title = "Computing the {CS} Decomposition of a
Partitioned Orthogonal Matrix",
journal = "Numerische Mathematik",
volume = "40",
pages = "297-306",
kwds = "nla, svd, csd, orthogonal matrix"
}
@techreport{stew:83,
author = "G. W. Stewart",
year = "1983",
title = "A Generalization of the {Eckart-Young} Approximation Theorem",
institution = "Department of Computer Science,
the University of Maryland",
number = "TR-1325",
kwds = "la, pert, matrix approximation, lsq, total least squares,
Schmidt-Mirsky theorem"
}
@techreport{stew:83a,
author = "G. W. Stewart",
year = "1983",
title = "A Nonlinear Version of {Gauss's} Minimum
Variance Theorem with Applications to
an Errors-in-the-Variables Model",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "TR-1263",
kwds = "la, eriv, total least squares, regr, lsq, nlop, pert, nllsq"
}
@inproceedings{stew:83b,
author = "G. W. Stewart",
year = "1983",
title = "A Method for Computing the Generalized Singular
Value Decomposition",
booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
pages = "207-220",
publisher = "Springer",
address = "New York",
kwds = "nla, svd, csd, gsvd"
}
@article{stew:83c,
author = "G. W. Stewart",
year = "1983",
title = "Computable Error Bounds for Aggregated {Markov} Chains",
journal = "Journal of the ACM",
volume = "30",
pages = "271--285",
kwds = "nla, Markov chain, eig, pert, aggregation"
}
@article{stew:84,
author = "G. W. Stewart",
year = "1984",
title = "Rank Degeneracy",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "5",
pages = "403-413",
kwds = "math, la, nla, collinearity, rank determination, condition"
}
@article{stew:84a,
author = "G. W. Stewart",
year = "1984",
title = "A Second Order Perturbation Expansion
for Small Singular Values",
journal = "Linear Algebra and Its Applications",
volume = "56",
pages = "231-235",
kwds = "la, svd, pert"
}
@article{stew:84b,
author = "G. W. Stewart",
year = "1984",
title = "On the Invariance of Perturbed Null
Vectors under Column Scaling",
journal = "Numerische Mathematik",
volume = "44",
pages = "61--65",
kwds = "la, pert, svd, null vector, total least squares"
}
@inproceedings{stew:84c,
author = "G. W. Stewart",
year = "1984",
title = "On the Structure of Nearly Uncoupled {Markov} Chains",
booktitle = "Mathematical Computer Performance and Reliability",
editor = "G. Iazeolla and P. J. Courtois and A. Hordijk",
pages = "287-302",
publisher = "Elsevier",
address = "New York",
kwds = "la, nearly uncoupled system, Markov chain, aggregation"
}
@article{stew:84d,
author = "G. W. Stewart",
year = "1984",
title = "On the Asymptotic Behavior of Scaled Singular
Value and {QR}~Decompostions",
journal = "Mathematics of Computation",
volume = "43",
pages = "483--489",
kwds = "la, qrd, svd, scaling"
}
@techreport{stsm:84,
author = "G. W. Stewart and W. J. Stewart and D. F. McAllister",
year = "1984",
title = "A Two-Stage Iteration for Solving Nearly Uncoupled
{Markov} Chains",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "TR-1384",
kwds = "nla, Markov chain, nearly uncoupled system, iter, aggregation"
}
@article{stew:85,
author = "G. W. Stewart",
year = "1985",
title = "A {Jacobi}-like Algorithm for Computing the
{Schur} Decomposition of a Non-{Hermitian} Matrix",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "28",
pages = "853-864",
kwds = "nla, prll, eig, Jacobi-like, Schur form, nonsymmetric matrix"
}
@article{stew:85b,
author = "G. W. Stewart",
year = "1985",
title = "A Note on Complex Division",
journal = "ACM Transactions on Mathematical Software",
volume = "11",
pages = "238--241",
kwds = "na, computer arithmetic, complex arithmetic"
}
@inproceedings{stew:86,
author = "G. W. Stewart",
year = "1986",
title = "Communcations in Parallel Algorithms: An Example",
booktitle = "Computer Science and Statistics: Proceedings
of the 18th Symposium on the Interface",
editor = "T. J. Boardman",
pages = "11-14",
kwds = "stat, nla, prll, communication, qrd"
}
@article{stew:87,
author = "G. W. Stewart",
year = "1987",
title = "A Parallel Implementation of the {QR}~Algorithm",
journal = "Parallel Computing",
volume = "5",
pages = "187-196",
kwds = "nla, eig, QR algorithm, prll"
}
@techreport{stew:87b,
author = "G. W. Stewart",
year = "1987",
title = "Invariant Subspaces and Capital Punishment",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "TR-1923",
kwds = "la, eig, pert, invariant subspace"
}
@techreport{stew:87c,
author = "G. W. Stewart",
year = "1987",
title = "An Iterative Method for Solving Linear Inequalities",
institution = "Computer Science Department, University of Maryland",
type = "Technical Report",
number = "TR-1833",
kwds = "la, nla, nlop, ginv, pert, iter, linear inequalities"
}
@article{stew:87d,
author = "G. W. Stewart",
year = "1987",
title = "Collinearity and Least Squares Regression",
journal = "Statistical Science",
volume = "2",
pages = "68-100",
kwds = "stat, lsq, regr, eriv, collinearity"
}
@article{stew:88,
author = "G. W. Stewart",
year = "1988",
title = "A Curiosity Concerning the Representation of Integers
in Noninteger Bases",
journal = "Mathematics of Computation",
volume = "51",
pages = "755--756",
kwds = "math, number theory"
}
@article{stew:89,
author = "G. W. Stewart",
year = "1989",
title = "On Scaled Projections and Pseudo-Inverses",
journal = "Linear Algebra and Its Applications",
volume = "112",
pages = "189--194",
kwds = "la, projection, ginv"
}
@techreport{stew:89b,
author = "G. W. Stewart",
year = "1989",
title = "Two Simple Residual Bounds for the Eigenvalues of
{Hermitian} Matrices",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "CS-TR 2364",
kwds = "la, eig, pert, residual bound, symmetric matrix"
}
@book{stsu:90,
author = "G. W. Stewart and J.-G. Sun",
year = "1990",
title = "Matrix Perturbation Theory",
publisher = "Academic Press",
address = "Boston",
kwds = "book, la, pert"
}
@inproceedings{stew:90,
author = "G. W. Stewart",
year = "1990",
title = "Perturbation Theory and Least Squares with Errors in
the Variables",
booktitle = "Contemporary Mathematics 112: Statistical
Analysis of Measurement Error Models and
Applications",
editor = "P. J. Brown and W. A. Fuller",
pages = "171--181",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
kwds = "stat, nla, pert, regr, lsq, eriv"
}
@techreport{stew:90b,
author = "G. W. Stewart",
year = "1990",
title = "An Updating Algorithm for Subspace Tracking",
institution = "Department of Computer
Science, University of Maryland",
type = "Technical Report",
number = "CS-TR 2494",
note = "To appear in IEEE Transactions on Signal Processing.",
kwds = "nla, condition, urvd, prll, rank determination"
}
@article{stew:90c,
author = "G. W. Stewart",
year = "1990",
title = "Communication and Matrix Computation on
Large Message Passing Systems",
journal = "Parallel Computing",
volume = "16",
pages = "27--40",
kwds = "nla, prll, communication, message passing"
}
@article{stew:90d,
author = "G. W. Stewart",
year = "1990",
title = "Stochastic Perturbation Theory",
journal = "SIAM Review",
volume = "32",
pages = "576--610",
kwds = "la, random matrix, pert, eig, lsq, svd, linear system"
}
@techreport{stew:91,
author = "G. W. Stewart",
year = "1991",
title = "On an Algorithm for Refining a Rank-Revealing
URV~Decomposition and a Perturbation Theorem for
Singular Values",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "CS-TR 2626",
note = "To appear in {\it Linear Algebra and Its Applications.\/}",
kwds = "la, nla, urvd, pert, svd, rank determination"
}
@techreport{stew:91a,
author = "G. W. Stewart",
year = "1991",
title = "Updating a Rank-Revealing {ULV}~Decomposition",
institution = "Department of Computer Science, University of Maryland",
type = "Technical Report",
number = "CS-TR 2627",
kwds = "la, nla, urvd, prll, condition, rank determination"
}
@inproceedings{stew:91c,
author = "G. W. Stewart",
year = "1990",
title = "Perturbation Theory for Nearly Uncoupled {Markov} Chains",
booktitle = "Numerical Methods for Markov Chains",
editor = "W. J. Stewart",
pages = "105--120",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, pert, Markov chain, eig"
}
@article{stzh:91,
author = "G. W. Stewart and G. Zhang",
year = "1991",
title = "On A Direct Method for the Solution of Nearly
Uncoupled {Markov} Chains",
journal = "Numerische Mathematik",
volume = "59",
pages = "1--11",
kwds = "nla, ldu, Markov chain, nearly uncoupled system"
}
@article{stzh:91a,
author = "G. W. Stewart and G. Zhang",
year = "1991",
title = "Eigenvalues of Graded Matrices and the Condition
of Numbers of a Multiple Eigenvalue",
journal = "Numerische Mathematik",
volume = "58",
pages = "703--712",
kwds = "la, pert"
}
@article{stie:52,
author = "E. Stiefel",
year = "1952",
title = "{\"Uber einige Methoden der Relaxationsrechnung}",
journal = "{Zeitschrift f\"ur angewandte Mathematik und
Physik}",
volume = "3",
pages = "1--33",
kwds = "nla, linear system, sparse, conjugate gradients, relaxation"
}
@article{stie:52a,
author = "E. Stiefel",
year = "1952/53",
title = "Ausgleichung ohne Aufstellung der Gausschen Normalgleichungen",
journal = "Wiss. Z. Technische Hochschule Dresden",
volume = "2",
pages = "441--442",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, Normal Equations, conjugate gradients, lsq"
}
@article{stie:55,
author = "E. Stiefel",
year = "1955",
title = "{Relaxationsmethoden besterr Strategie zur L\"osung
linearer Gleichungssysteme}",
journal = "Commentarii Mathematici Helvetici",
volume = "29",
pages = "157--179",
kwds = "nla, linear system, iter, relaxation"
}
@article{stig:77,
author = "S. M. Stigler",
year = "1977",
title = "An Attack on {Gauss}, Published by {Legendre} in 1820",
journal = "Historia Mathematica",
volume = "4",
pages = "31-35",
kwds = "history, Gauss, lsq, Legendre, regr"
}
@book{stig:86,
author = "S. M. Stigler",
year = "1986",
title = "The History of Statistics",
publisher = "Harvard University Press",
address = "Cambridge, Massachusetts",
kwds = "book, stat, lsq, history, regr"
}
@article{stoe:64,
author = "J. Stoer",
year = "1964",
title = "On the Characteristics of Least Upper Bound Norms
in Matrix Space",
journal = "Numerische Mathematik",
volume = "6",
pages = "302--314",
kwds = "la, norm"
}
@article{stoe:71,
author = "J. Stoer",
year = "1971",
title = "On the Numerical Solution of Constrained Least-Squares
Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "8",
pages = "382--411",
kwds = "nla, lsq, constraints"
}
@article{ston:62,
author = "B. J. Stone",
year = "1962",
title = "Best Possible Ratios of Certain Matrix Norms",
journal = "Numerische Mathematik",
volume = "4",
pages = "114--116",
kwds = "la, norm"
}
@article{ston:73,
author = "H. S. Stone",
year = "1973",
title = "An Efficient Parallel Algorithm for the Solution of a Tridiagonal
Linear System of Equations",
journal = "Journal of the {ACM}",
volume = "20",
pages = "27--38",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, tridiagonal matrix"
}
@article{ston:75,
author = "H. Stone",
year = "1975",
title = "Parallel Tridiagonal Equation Solvers",
journal = "ACM Transactions on Mathematical Software",
volume = "1",
pages = "289-307",
kwds = "nla, prll, tridiagonal matrix"
}
@book{stra:76,
author = "G. Strang",
year = "1976",
title = "Linear Algebra and Its Applications",
publisher = "Academic Press",
address = "New York",
kwds = "book, la"
}
@article{stra:69,
author = "V. Strassen",
year = "1969",
title = "{G}aussian Elimination is Not Optimal",
journal = "Numerische Mathematik",
volume = "13",
pages = "354--356",
note = "Cited in \cite{govl:89}.",
kwds = "nla, lud, linear system, fast algorithm, complexity"
}
-su-
@inproceedings{suri:91,
author = "J. C. S. Lui and R. R. Muntz",
year = "1991",
title = "Numerical Comparison of the Replacement Process
Approach with the Aggregation -Disaggregation
Algorithm for Row-Continuous {Markov} Chains",
booktitle = "Numerical Solution of {Markov} Chains",
editor = "W. J. Stewart",
pages = "287--302",
publisher = "North Holland",
address = "Amsterdam",
kwds = "nla, Markov chain, aggregation"
}
@unpublished{sun:79,
author = "J.-G. Sun",
year = "1979",
title = "A Theorem on the Perturbation of Generalized Eigenvalues",
note = "Report on the Conference Numerical Mathematics, Guangzhou, China",
kwds = "la, pert, geig"
}
@article{sun:80,
author = "J.-G. Sun",
year = "1980",
title = "Invariant Subspaces and Generalized Invariant Subspaces
(II)",
journal = "Math. Numer. Sinica",
volume = "2",
pages = "113--123",
note = "Cited in \cite{elsu:82}",
kwds = "la, pert, geig, invariant subspace"
}
@article{sun:82,
author = "J.-G. Sun",
year = "1982",
title = "A Note on {Stewart's} Theorem for Definite Matrix Pairs",
journal = "Linear Algebra and Its Applciations",
volume = "48",
pages = "331--339",
kwds = "la, geig, pert, symmetric matrix"
}
@inproceedings{sun:83,
author = "J.-G. Sun",
year = "1983",
title = "Perturbation Analysis for the Generalized Eigenvalue Problem
and the Generalized Singular Value Problem",
booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
pages = "221--244",
publisher = "Springer Verlag",
address = "New York",
kwds = "la, geig, gsvd, pert"
}
@article{sun:83a,
author = "J.-G. Sun",
year = "1983",
title = "Perturbation Bounds for Eigenspaces of a Definite
Matrix Pair",
journal = "Numerische Mathematik",
volume = "41",
pages = "321--343",
kwds = "la, geig, pert, symmetric matrix"
}
@article{sun:83b,
author = "J.-G. Sun",
year = "1983",
title = "Perturbation Analysis for the Generalized Singular
Value Decomposition",
journal = "SIAM Journal on Numerical Analysis",
volume = "20",
pages = "611--625",
kwds = "la, pert, gsvd"
}
@article{sun:84,
author = "J.-G. Sun",
year = "1984",
title = "Estimation of the Separation of Two Matrices",
journal = "Journal of Computational Mathematics",
volume = "2",
pages = "189--200",
kwds = "la, pert, eig"
}
@article{sun:84b,
author = "J.-G. Sun",
year = "1984",
title = "On the Perturbation of the Eigenvalues of a Normal Matrix",
journal = "Math. Numer. Sinca",
volume = "6",
pages = "334--336",
kwds = "la, pert, eig, normal matrix"
}
@article{sun:85,
author = "J.-G. Sun",
year = "1985",
title = "{Gerschgorin} Type Theorem and the Perturbation of the
Eigenvalues of a Singular Pencil",
journal = "Math. Numer. Sinica",
volume = "7",
pages = "253--264",
note = "In Chinese. Translation in {\it Chinese Journal of
Numerical Mathematics and Applications} {\bf 10} (1988) 1--13.",
kwds = "la, geig, pert, Gerschgorin's theorem, matrix pencil"
}
@article{sun85a,
author = "J.-G. Sun",
year = "1985",
title = "Eigenvalues and Eigenvectors of a Matrix Dependent
on Several Parameters",
journal = "Journal of Computational Mathematics",
volume = "3",
pages = "351--364",
kwds = "na, pert, eig"
}
@book{sun:87,
author = "J.-G. Sun",
year = "1987",
title = "Matrix Perturbation Analysis",
publisher = "Academic Press",
address = "Beijing",
note = "In Chinese.",
kwds = "book, la, pert"
}
@article{sun:88,
author = "J.-G. Sun",
year = "1988",
title = "A Note on Simple Non-Zero Singular Values",
journal = "Journal of Computational Mathematics",
volume = "6",
pages = "258--266",
kwds = "la, pert, svd"
}
@article{sun:88a,
author = "J.-G. Sun",
year = "1988",
title = "Sensitivity Analysis of Multiple Eigenvalues.~{I}",
journal = "Journal of Computational Mathematics",
volume = "6",
pages = "28--38",
note = "Cited in \cite{sun:89}",
kwds = "la, eig, pert, multiple eigenvalue"
}
@article{sun:89,
author = "J.-G. Sun",
year = "1989",
title = "A Note on Local Behavior of Multiple Eigenvalues",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "10",
pages = "533--541",
kwds = "la, pert, eig, multiple eigenvalue"
}
@article{sun:91,
author = "J.-G. Sun",
year = "1991",
title = "Perturbation Bounds for the {Cholesky} and
{QR} Factorizations",
journal = "BIT",
volume = "31",
pages = "341--352",
kwds = "la, pert, qrd, lud"
}
@techreport{sun:91a,
author = "J.-G. Sun",
year = "1991",
title = "Eigenvalues of Rayleigh Quotient Matrices",
institution = "Department of Mathematics, {Link\"oping} Univeristy",
type = "Technical Report",
number = "LiTH-MAT-R-1991-25",
kwds = "la, eig, pert, residual bound"
}
@article{sun:92,
author = "J.-G. Sun",
year = "1992",
title = "On Condition Numbers of a Nondefective Multiple Eigenvalue",
journal = "Numerische Mathematik",
volume = "61",
pages = "265--275",
kwds = "la, eig, pert"
}
@techreport{sun:92a,
author = "J.-G. Sun",
year = "1992",
title = "Backward Perturbation Analysis of Certain
Characteristic Subspaces",
institution = "Department of Mathematics, {Link\"oping} Univeristy",
type = "Technical Report",
number = "LiTH-MAT-R-1992-12",
kwds = "la, eig, pert, invariant subspace, backward perturbation"
}
-sv- -sw-
@article{swan:61,
author = "C. A. Swanson",
year = "1961",
title = "An Inequality for Linear Transformations with
Eigenvalues",
journal = "Bulletin of the American Mathematical Society",
volume = "67",
pages = "607--608",
kwds = "la, eig, pert, symmetric matrix"
}
@article{swsw:73,
author = "P. N. Swarztrauber and R. A. Sweet",
year = "1973",
title = "The Direct Solution of the Discrete {P}oisson Equation on a Disk",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "10",
pages = "900--907",
note = "Cited in \cite{govl:89}.",
kwds = "nla, direct Poisson solver, Poisson's equation"
}
@article{swar:79,
author = "P. N. Swarztrauber",
year = "1979",
title = "A Parallel Algorithm for Solving General Tridiagonal Equations",
journal = "Mathematics of Computation",
volume = "33",
pages = "185--199",
note = "Cited in \cite{govl:89}.",
kwds = "nla, prll, linear system, tridiagonal matrix"
}
@article{swee:74,
author = "R. A. Sweet",
year = "1974",
title = "A Generalized Cyclic Reduction Algorithm",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "11",
pages = "506--520",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, cyclic reduction"
}
@article{swee:77,
author = "R. A. Sweet",
year = "1977",
title = "A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems
of Arbitrary Dimension",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "14",
pages = "706--720",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, cyclic reduction, block algorithm,
block tridiagonal matrix"
}
@article{swbo:72,
author = "B. F. Swindel and D. R. Bower",
year = "1972",
title = "Rounding Errors in the Independent Variables in a General
Linear Model",
journal = "Technometrics",
volume = "14",
pages = "215--218",
kwds = "stat, regr, eriv, rounding error"
}
@article{swin:81,
author = "B. F. Swindel",
year = "1981",
title = "Geometry of Ridge Regression",
journal = "The Americal Statistician",
volume = "35",
pages = "12-15",
kwds = "stat, regr, ridge regression"
}
-sx- -sy-
@article{sylv:1852,
author = "J. J. Sylvester",
year = "1852",
title = "A Demonstration of the Theorem that Every Homogeneous
Quadratic Polynomial is Reducible by Real Orthogonal
Substitutions to the Form of a Sum of Positive and
Negative Squares",
journal = "Philosopical Magazine",
volume = "2",
pages = "138--142",
kwds = "la, inertia, Sylvester-Jacobi inertia theorem"
}
@article{sylv:1853,
author = "J. J. Sylvester",
year = "1853",
title = "On a Theory of the Syzygetic Relations etc.",
journal = "Phil. Trans.",
volume = "",
pages = "481-84",
note = "Cited in \cite{borc:1857}.",
kwds = "la, inertia, Sylvester-Jacobi inertia theorem"
}
@article{sylv:1889,
author = "J. J. Sylvester",
year = "1889",
title = "A New Proof That a General Quadric May Be Reduced
to Its Canonical Form (That Is, a Linear Function of
Squares) by Means of a Real Orthogonal Substitution",
journal = "Messenger of Mathematics",
volume = "19",
pages = "1--5",
kwds = "math, la, svd"
}
@article{sylv:1889a,
author = "J. J. Sylvester",
year = "1889",
title = "Sur la r\'eduction biorthogonale d'une forme
lin\'eo-lin\'eaire \`a sa forme cannonique",
journal = "Comptes Rendus de l'Academie des Sciences, Paris",
volume = "108",
pages = "651--653",
kwds = "la, svd"
}
@article{sylv:1889b,
author = "J. J. Sylvester",
year = "1889",
title = "On the Reduction of a Bilinear Quantic of the
$n^{\mbox{\sc th}}$ Order to the Form of a Sum of $n$
Products by a Double Orthogonal Substitution",
journal = "Messenger of Mathematics",
volume = "19",
pages = "42--46",
kwds = "math, la, svd"
}
@article{sywi:80,
author = "H. J. Symm and J. H. Wilkinson",
year = "1980",
title = "Realistic Error Bounds for a Simple Eigenvalue and Its Associated
Eigenvector",
journal = "Numerische Mathematik",
volume = "35",
pages = "113--126",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, eig"
}
-sz-
@book{szeg:67,
author = "G. Szeg{\"o}",
year = "1967",
title = "Orthogonal Polynomials",
edition = "Third",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
kwds = "book, orthogonal polynomial"
}
@book{szna:60,
author = "Sz.-Nagy, Bela",
year = "1960",
title = "Extensions of Linear Transformations in {Hilbert} Space
which Extend beyond This Space",
publisher = "Ungar",
address = "New York",
note = "An appendix to Riesz and Sz.-Nagy \cite{ries:55}
issued as a separate pamphlet.",
kwds = "book, functional analysis"
}
-ta-
@article{tabe:1893,
author = "H. Taber",
year = "1893",
title = "On the Linear Transformations between Two Quadratics",
journal = "Proceedings of the London Mathematical Society",
pages = "290-306",
kwds = "la"
}
@phdthesis{taka:72,
author = "Y. Takahashi",
year = "1972",
title = "Some Problems for Applications of {Markov} Chains",
school = "Tokyo Institute of Technology",
note = "Cited in \cite{taka:84}.",
kwds = "nla, Markov chain, aggregation, relaxation"
}
@article{taka:74,
author = "Y. Takahashi",
year = "1974",
title = "A Sequencing Model with an Application to Speed Class
Sequencing in Air Traffic Control",
journal = "J. Operations Research Society of Japan",
volume = "17",
pages = "1--28",
note = "Cited in \cite{taka:84}.",
kwds = "nla, Markov chain, aggregation, relaxation"
}
@techreport{taka:75,
author = "Y. Takahashi",
year = "1975",
title = "A Lumping Method for Numerical Calculations of Stationary
Distributions of {Markov} Chains",
institution = "Department of Information Sciences, Tokyo Institute
of Technology",
type = "Research Report",
number = "B-18",
kwds = "nla, Markov chain, aggregation"
}
@inproceedings{taka:84,
author = "Y Takahashi",
year = "1984",
title = "Weak {D}-{Markov} Chain and Its Application to a Queuing
Network",
booktitle = "Mathematical Computer Performance and Reliability",
editor = "G. Iazeolla and P. J. Courtois and A. Hordijk",
pages = "153--166",
publisher = "Elsevier",
address = "New York",
kwds = "nla, Markov chain"
}
@article{tana:69,
author = "K. Tanabe",
year = "1969",
title = "Projection Method for Solving a Singular System
of Linear Equations and its Applications",
journal = "Numerische Mathematik",
volume = "17",
pages = "203--214",
kwds = "nla, singular system, Kaczmarz's method, projection method"
}
@article{tana:74,
author = "K. Tanabe",
year = "1974",
title = "Characterizatio of Linear Stationary Iterative Process
for Solving a Singular System of Linear Equations",
journal = "Numerische Mathematik",
volume = "22",
pages = "349--359",
kwds = "nla, singular system, iter"
}
@article{tana:75,
author = "K. Tanabe",
year = "1975",
title = "Neumann-Type Expansions of Reflexive Generalized Inverses
of a Matrix and the Hyperpower Iterative Method",
journal = "Linear Algebra and Its Applications",
volume = "10",
pages = "163--175",
kwds = "nla, ginv, iter, Neumann series"
}
@article{tago:81,
author = "W. P. Tang and G. H. Golub",
year = "1981",
title = "The Block Decomposition of a {V}andermonde Matrix and
Its Applications",
journal = "{BIT}",
volume = "21",
pages = "505--517",
note = "Cited in \cite{govl:89}.",
kwds = "nla, vandermonde matrix, block algorithm"
}
@techreport{tath:80,
author = "M. A. Tanner and R. A. Thisted",
year = "1980",
title = "A Remark on {AS}~127: Generation of Random Orthogonal Matrices",
institution = "Department of Statistics, University of Chicago",
number = "112",
kwds = "stat, la, random matrix, orthogonal matrix"
}
@article{tapi:71,
author = "R. A. Tapia",
year = "1971",
title = "The {Kantorovich} Theorem for {Newton's} Method",
journal = "American Mathematical Monthly",
volume = "78",
pages = "389--392",
kwds = "nlop, Kantorovich theorem, Newton's method"
}
@article{taus:48,
author = "O. Taussky",
year = "1948",
title = "Bounds for Characteristic Roots of Matrices",
journal = "Duke Mathematical Journal",
volume = "15",
pages = "1043--1044",
kwds = "la, pert, eig, Gerschgorin's theorem, irreducible matrix"
}
@article{taus:49,
author = "O. Taussky",
year = "1949",
title = "A Recurring Theorem on Determinants",
journal = "American Mathematical Monthly",
volume = "46",
pages = "672--675",
kwds = "la, eig, Gerschgorin's theorem, history, determinant"
}
-tb- -tc- -td- -te-
@article{tela:77,
author = "J. Terray and P. Lancaster",
year = "1977",
title = "On the Numerical Calculation of Eigenvalues and
Eigenvectors of Operator Polynomials",
journal = "Journal of Mathematical Analysis and Applications",
volume = "60",
pages = "370--378",
kwds = "nla, geig, matrix polynomial"
}
@article{tewa:69,
author = "R. P. Tewarson",
year = "1969",
title = "Projection Methods for Solving Sparse Linear Systems",
journal = "Computer Journal",
volume = "",
pages = "77--80",
kwds = "nla, sparse, iter, Kaczmarz's method, projection method"
}
-tf- -tg- -th-
@article{thom:92,
author = "R. C. Thompson",
year = "1992",
title = "High, Low, and Quantitative Roads in Linear Algebra",
journal = "Linear Algebra and Its Applications",
volume = "162--164",
pages = "23--64",
kwds = "la"
}
@article{thwe:70,
author = "G. L. Thompson and R. L. Weil",
year = "1970",
title = "Reducing the Rank of {$A - \lambda B$}",
journal = "Proceedings of the American Mathematical Society",
volume = "26",
pages = "548--554",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig"
}
@article{thwe:72,
author = "G. L. Thompson and R. L. Weil",
year = "1972",
title = "Roots of Matrix Pencils {$Ay = \lambda By$}: Existence,
Calculations, and Relations to Game Theory",
journal = "Linear Algebra and its Applications",
volume = "5",
pages = "207--226",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, game theory"
}
-ti-
@article{tiho:63,
author = "A. N. Tihonov",
year = "1963",
title = "Regularization of Incorrectly Posed Problems",
journal = "Soviet Mathematics",
volume = "4",
pages = "1624--1627",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "na, ill-posed problem, regularization"
}
-tj- -tk- -tl- -tm- -tn- -to-
@article{todd:50,
author = "J. Todd",
year = "1950",
title = "The Condition of a Certain Matrix",
journal = "Proceedings of the Cambridge Philosophical Society",
volume = "46",
pages = "116--118",
kwds = "nla, pert, condition"
}
@article{todd:54,
author = "J. Todd",
year = "1954",
title = "The Condition of Certain Matrices~{II}",
journal = "Archiv der Mathematik",
volume = "5",
pages = "249--257",
kwds = "la, pert, condition"
}
@article{toep:18,
author = "O. Toeplitz",
year = "1918",
title = "Das algebraische {A}nalogon zu einem {S}atze
von {F}ej{\'e}r",
journal = "Mathematische Zeitschrift",
volume = "2",
pages = "187-197",
kwds = "la, field of values"
}
@article{toin:87,
author = "P. L. Toint",
year = "1987",
title = "On Large Scale Nonlinear Least Squares Calculations",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "8",
pages = "416--435",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, sparse, lsq, nllsq"
}
@article{torn:64,
author = "L. Tornheim",
year = "1964",
title = "Convergence of Multipoint Iterative Methods",
journal = "Journal of the ACM",
volume = "11",
pages = "210--220",
kwds = "nlop, multipoint method, iter"
}
-tp- -tq- -tr-
@article{trau:64,
author = "J. F. Traub",
year = "1964",
title = "On {Lagrange-Hermite} Interpolation",
journal = "Journal of the Society for Industrial and Applied Mathematics",
volume = "12",
pages = "886--891",
kwds = "na, interpolation"
}
@article{trau:65,
author = "J. F. Traub",
year = "1965",
title = "Solution of Linear Difference and Differential Equations",
journal = "Bulletin of the American Mathematical Society",
volume = "71",
pages = "538--541",
kwds = "na, difference equation, ode"
}
@article{trau:66,
author = "J. F. Traub",
year = "1966",
title = "Associated Polynomials and Uniform Methods for the
Solution of Linear Problems",
journal = "SIAM Review",
volume = "8",
pages = "277--301",
kwds = "nlop, polynomial, difference equation, ode"
}
@article{trau:66a,
author = "J. F. Traub",
year = "1966",
title = "A Class of Globally Convergent Iteration Functions for the
Solution of Polynomial Equations",
journal = "Mathematics of Computation",
volume = "20",
pages = "1966",
kwds = "nlop, polynomial"
}
@inproceedings{trau:67,
author = "J. F. Traub",
year = "1967",
title = "The Calculation of Zeros of Polynomial and Analytic
Functions",
booktitle = "Proceedings of Symposia in Applied Mathematics,
Volume~19, Mathemtical Aspects of Computer Science",
editor = "",
pages = "138--152",
publisher = "Anmerican Mathematical Society",
address = "Providence, Rhode Island",
kwds = "nlop, polynomial"
}
@article{trsc:1990,
author = "L. N. Trefethen and R. S. Schreiber",
year = "1990",
title = "Average-Case Stability of {Gaussian} Elimination",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "11",
pages = "335--360",
kwds = "nla, lud, rounding error"
}
@unpublished{tref:90,
author = "L. N. Trefethen",
year = "1990",
title = "Non-Normal Matrices and Pseudo-Eigenvalues",
note = "Manuscript, Department of Computer Science, Cornell
University",
kwds = "la, nla, pert, eig, svd, matrix powers"
}
@article{tren:64,
author = "W. F. Trench",
year = "1964",
title = "An Algorithm for the Inversion of Finite {T}oeplitz Matrices",
journal = "J. SIAM",
volume = "12",
pages = "515--522",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, toeplitz matrix"
}
@article{tren:67,
author = "W. F. Trench",
year = "1967",
title = "Weighting Coefficients for the Prediction of Stationary
Time Series from the Finite Past",
journal = "SIAM Journal on Applied Mathematics",
volume = "15",
pages = "1502--1510",
kwds = "nla, Toeplitz matrix, Trench's method, linear system, weights,
fast algorithm"
}
@article{tren:74,
author = "W. F. Trench",
year = "1974",
title = "Inversion of {T}oeplitz Band Matrices",
journal = "Mathematics of Computation",
volume = "28",
pages = "1089--1095",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, toeplitz matrix, band matrix"
}
@book{tric:70,
author = "F. G. Tricomi",
year = "1970",
title = "{Vorlesungen \"uber Orthogonalreihen}",
edition = "Second",
publisher = "Springer",
address = "New York",
kwds = "book, orthogonal polynomial"
}
@book{triv:82,
author = "K. S. Trivedi",
year = "1982",
title = "Probability and Statistics with Reliability, Queuing,
and Computer Science Applications",
publisher = "Prentice--Hall",
address = "Englewook Cliffs, NJ",
kwds = "book, queue, Markov chain"
}
-ts-
@article{tsao:75,
author = "N.-K. Tsao",
year = "1975",
title = "A Note on Implementing the {Householder} Transformation",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "53--58",
kwds = "nla, Householder transformation"
}
@article{tsit:89,
author = "J. H. Tsitsiklis",
year = "1989",
title = "{Markov} Chains with Rare Transitions and Simulated
Annealing",
journal = "Mathematics of Operations Research",
volume = "14",
pages = "70--90",
kwds = "nla, eig, Markov chain, simulated annealing"
}
-tt- -tu-
@inproceedings{tppl:85,
author = "J. Tuazon and J. Peterson and M. Pniel and D. Lieberman",
year = "1985",
title = "Caltech/{JPL} Hypercube Concurrent Processor",
booktitle = "Proceedings of 1985 International Conference on
Parallel Computing",
kwds = "prll, architecture, hypercube"
}
@book{tuck:67,
author = "H. G. Tucker",
year = "1967",
title = "A Graduate Course in Probability",
publisher = "Academic Press",
address = "New York",
kwds = "book, probability"
}
@book{tuai:32,
author = "H. W. Turnbull and A. C. Aitken",
year = "1932",
title = "An Introduction to the Theory of Canonical
Matrices",
publisher = "Blackie \& Son",
address = "London",
kwds = "book, la, history"
}
@article{turi:48,
author = "A. M. Turing",
year = "1948",
title = "Rounding-off Errors in Matrix Processes",
journal = "The Quarterly Journal of Mechanics and Applied Mathematics",
volume = "1",
pages = "287-308",
kwds = "math, nla, lud, rounding error, condition"
}
@article{turn:91,
author = "K. Turner",
year = "1991",
title = "Computing Projections for the Karmarkar Algorithm",
journal = "Linear Algebra and Its Applications",
volume = "152",
pages = "141--154",
kwds = "nla, nlop, Karmarkar algorithm, projection"
}
-tv- -tw- -tx- -ty- -tz-
-ua- -ub- -uc- -ud- -ue- -uf- -ug- -uh-
@article{uhli:73,
author = "F. Uhlig",
year = "1973",
title = "Simultaneous Block Diagonalization of Two Real Symmetric Matrices",
journal = "Linear Algebra and its Applications",
volume = "7",
pages = "281--289",
note = "Cited in \cite{govl:89}.",
kwds = "la, geig, block algorithm"
}
@article{uhli:76,
author = "F. Uhlig",
year = "1976",
title = "A Canonical Form for a Pair of Real Symmetric Matrices that
Generate a Nonsingular Pencil",
journal = "Linear Algebra and its Applications",
volume = "14",
pages = "189--210",
note = "Cited in \cite{govl:89}.",
kwds = "la, geig, symmetric matrix"
}
@article{uhli:79,
author = "F. Uhlig",
year = "1979",
title = "A Recurring Theorem about Pairs of Quadratic Forms and Extensions:
A Survey",
journal = "Linear Algebra and Its Applications",
volume = "25",
pages = "219-237",
kwds = "math, la, geig, symmetric matrix"
}
@article{uhli:92,
author = "F. Uhlig",
year = "1992",
title = "Are the Coefficients of a Polynomial Well-Conditioned
Functions of Its Roots",
journal = "Numerische Mathematik",
volume = "61",
pages = "383--393",
kwds = "nlop, polynomial, condition"
}
-ui- -uj- -uk- -ul- -um- -un-
@techreport{unde:75,
author = "R. Underwood",
year = "1975",
title = "An Iterative Block {L}anczos Method for the Solution
of Large Sparse Symmetric Eigenproblems",
number = "STAN-CS-75-496",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, block algorithm, sparse, eig"
}
-uo- -up- -uq-
-ur- -us- -ut- -uu- -uv- -uw- -ux- -uy- -uz-
-va-
@proceedings{vacc:91,
year = "1990",
title = "SVD and Signal Processing, {II}",
editor = "R. J. Vaccaro",
publisher = "Elsevier Science Publishers",
address = "Amsterdam"
}
@techreport{vdge:87,
author = "van de Geijn, R. A.",
year = "1987",
title = "Implementing the {QR}-Algorithm on an Array of Processors",
institution = "Department of Computer Science, University of
Maryland",
type = "Technical Report",
number = "1897",
kwds = "nla, prll, qrd, QR algorithm, eig, systolic"
}
@unpublished{vdge:90,
author = "R. A. van de Geijn",
year = "1990",
title = "Deferred Shifting Schemes for Parallel {QR} Methods",
note = "Manuscript, Department of Computer Science, University of Texas
at Austin",
kwds = "nla, eig, QR algorithm, prll"
}
@article{vand:71,
author = "J. S. Vandergraft",
year = "1971",
title = "Generalized {Rayleigh} Methods with Applications to
Finding Eigenvalues of Large Matrices",
journal = "Linear Algebra and Its Applications",
volume = "4",
pages = "353--368",
kwds = "nla, eig, sparse, Rayleigh-Ritz method, symmetric matrix"
}
@article{vdsl:69,
author = "van der Sluis, A.",
year = "1969",
title = "Condition Numbers and Equilibration of Matrices",
journal = "Numerische Mathematik",
volume = "14",
pages = "14--23",
kwds = "nla, pert, lsq, condition, scaling"
}
@article{vdsl:70,
author = "van der Sluis, A.",
year = "1970",
title = "Stability of Solutions of Linear Algebraic Systems",
journal = "Numerische Mathematik",
volume = "14",
pages = "246--251",
kwds = "nla, pert, linear system, condition"
}
@article{vdsl:70a,
author = "van der Sluis, A.",
year = "1970",
title = "Condition, Equilibration, and Pivoting in Linear
Algebraic Systems",
journal = "Numerische Mathematik",
volume = "15",
pages = "74--86",
kwds = "nla, pert, linear system, pivoting, condition"
}
@article{vdsl:75,
author = "van der Sluis, A.",
year = "1975",
title = "Stability of the Solutions of Linear Least Squares
Problems",
journal = "Numerische Mathematik",
volume = "23",
pages = "241--254",
kwds = "nla, pert, lsq"
}
@article{vdsl:75a,
author = "van der Sluis, A.",
year = "1975",
title = "Perturbations of Eigenvalues of Nonnormal Matrices",
journal = "Communications of the {ACM}",
volume = "18",
pages = "30--36",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, eig, nonnormal matrix"
}
@article{vdsl:76,
author = "van der Sluis, A.",
year = "1976",
title = "Estimating the Solutions of Slowly Varying Recursions",
journal = "SIAM Journal on Mathematical Analysis",
volume = "7",
pages = "662--695",
kwds = "na, difference equation"
}
@article{vdve:79,
author = "van der Sluis, A. and G. W. Veltkamp",
year = "1979",
title = "Restoring Rank and Consistency by Orthogonal Projection",
journal = "Linear Algebra and Its Applications",
volume = "28",
pages = "257--278",
kwds = "nla, linear system, projection, rank determination"
}
@article{vdvd:86,
author = "van der Sluis, A. and Van der Vorst, H. A.",
year = "1986",
title = "The Rate of Convergence of Conjugate Gradients",
journal = "Numerische Mathematik",
volume = "48",
pages = "543--560",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients"
}
@techreport{vdsl:91,
author = "van der Sluis, A.",
year = "1991",
title = "The Convergenc Behavior of Conjugate Gradients
and Ritz Values in Various Circumstances",
institution = "Department of Mathematics, University Utrecht",
type = "Preprint",
number = "691",
kwds = "nla, eig, linear system, conjugate gradients"
}
@article{vdve:77,
author = "Van de Vel, H.",
year = "1977",
title = "Numerical Treatment of a Generalized {V}andermonde System of
Equations",
journal = "Linear Algebra and its Applications",
volume = "17",
pages = "149--174",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, Vandermonde matrix"
}
@article{vdvo:81,
author = "van der Vorst, H. A.",
year = "1981",
title = "Iterative Solution Methods for Certain Sparse
Linear Systems with a Non-Symmetric Matrix
Arising from {PDE}-Problems",
journal = "Journal of Computational Physics",
volume = "44",
pages = "1--19",
kwds = "nla, iter, linear system, nonsymmetric matrix, sparse"
}
@article{vdvo:82,
author = "van der Vorst, H. A.",
year = "1982",
title = "A Vectorizable Variant of Some {ICCG} Methods",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "3",
pages = "350--356",
kwds = "nla, linear system, conjugate gradients, incomplete factorization,
preconditioning"
}
@phdthesis{vdvo:82a,
author = "van der Vorst, H. A.",
year = "1982",
title = "Preconditioning by Incomplete Decompositions",
school = "University of Utrecht",
kwds = "nla, linear system, conjugate gradients, incomplete factorization,
preconditioning"
}
@article{vdvo:82b,
author = "Van der Vorst, H. A.",
year = "1982",
title = "A Generalized {L}anczos Scheme",
journal = "Mathematics of Computation",
volume = "39",
pages = "559--562",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm"
}
@article{vdwa:27,
author = "van der Warden, B. L.",
year = "1927",
title = " {Ein Satz \"uber Klasseneinteilungen von Endlicher Mengen}",
journal = " {Abhandlungen aus dem Mathematischen Seminar der
Hamburgischen Universit\"at}",
volume = "5",
pages = "185--188",
kwds = "math, Koenig-Frobenius theorem"
}
@article{vdoo:79,
author = "Van Dooren, P.",
year = "1979",
title = "The Computation of {Kronecker's} Canonical Form of a
Singular Pencil",
journal = "Linear Algebra and Its Applications",
volume = "27",
pages = "103--140",
kwds = "la, pert, geig, Kronecker form, matrix pencil"
}
@article{vdoo:81,
author = "Van Dooren, P.",
year = "1981",
title = "The Generalized Eigenstructure Problem in
Linear System Theory",
journal = "IEEE Transactions on Automatic Control",
volume = "26",
pages = "111--129",
kwds = "la, geig, control"
}
@article{vdoo:81a,
author = "Van Dooren, P.",
year = "1981",
title = "A Generalized Eigenvalue Approach for Solving {R}iccati Equations",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "2",
pages = "121--135",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, Riccati equation"
}
@incollection{vdoo:83,
author = "Van Dooren, P.",
year = "1983",
title = "Reducing Subspaces: definitions, properties and Algorithms",
booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
publisher = "Springer-Verlag",
address = "New York",
pages = "58--73",
note = "Cited in \cite{govl:89}.",
kwds = "la, nla, reducing subspaces, geig"
}
@article{vdve:88,
author = "Van Dooren, P. and M. Verhaegen",
year = "1988",
title = "Condensed Forms for Efficient Time-Invariant
{Kalman} Filtering",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "9",
pages = "516-530",
kwds = "nla, Kalman filter, time series"
}
@phdthesis{vhuf:87,
author = "Van Huffel, S.",
year = "1987",
title = "Analysis of the Total Least Squares Problem
and Its Use in Parameter Estimation",
school = "Katholeike Universiteit Leuven",
kwds = "la, nla, regr, lsq, total least squares"
}
@article{vhva:87,
author = "S. {Van Huffel} and J. Vandervalle",
year = "1987",
title = "Algebraic Relationships Between Classical Regression and Total
Least-squares Estimation",
journal = ". Linear Algebra and its Applications",
volume = "93",
pages = "149--162",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, total least squares, lsq, regr"
}
@article{vhva:87a,
author = "Van Huffel, S. and J. Vandewalle",
year = "1987",
title = "Subset Selection Using the Total Least Squares Approach in
Collinearity Problems with Errors in the Variables",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "695--714",
note = "Cited in \cite{govl:89}.",
kwds = "nla, total least squares, subset selection, collinearity,
eriv"
}
@article{vhvh:87,
author = "S. {Van Huffel} and J. Vandervalle and A. Haegemans",
year = "1987",
title = "An Effficient and Reliable Algorithm for Computing the Singular
Subspace of a Matrix, Associated with its Smallest Singular Values",
journal = "J. Comp. and Appl. Math.",
volume = "19",
pages = "313--330",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, total least squares, svd"
}
@techreport{vhuf:88,
author = "Van Huffel, S.",
year = "1988",
title = "Comments on the Solution of the Nongeneric Total Least Squares
Problem",
number = "ESAT-KUL-88/3",
institution = "Department of Electrical Engineering, Katholieke
Universiteit Leuven",
address = "Leuven, Belgium",
note = "Cited in \cite{govl:89}.",
kwds = "nla, total least squares"
}
@article{vhva:88,
author = "Van Huffel, S. and J. Vandewalle",
year = "1988",
title = "The Partial Total Least Squares Algorithm",
journal = "Journal of Computational and Applied Mathematics",
volume = "21",
pages = "333--342",
note = "Cited in \cite{govl:89}.",
kwds = "nla, total least squares"
}
@article{vhva:88a,
author = "S. {Van Huffel} and J. Vandervalle",
year = "1988",
title = "Analysis and Solution of the Nongeneric Total Least Squares
Problem",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "9",
pages = "360--372",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, total least squares"
}
@article{vhva:89,
author = "S. {Van Huffel} and J. Vandervalle",
year = "1989",
title = "Analysis and Properties of the Generalized Total Least
Squares Problem {$AX \approx B$} when Some or all Columns
in {$A$} are Subject to Error",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "10",
pages = "294--315",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, total least squares"
}
@article{vhzh:91,
author = "Van Huffel, S. and H. Zha",
year = "1991",
title = "The Restricted Total Least Squares Problem:
Formulation, Algorithm, and Properties",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "12",
pages = "292--309",
kwds = "nla, total least squares, gsvd"
}
@techreport{vhzh:91a,
author = "Van Huffel, S. and H. Zha",
year = "1991",
title = "An Efficient Total Least Squares Algorithm Based
on a Rank-Revealing Two-Sided Orthogonal Decomposition",
institution = "Department of Electrical Engineering, Katholieke
Universiteit Leuven",
type = "ESAT-SISTA Report",
number = "1991-08",
kwds = "nla, total least squares, urvd"
}
@book{vhva:91,
author = "Van Huffel, S. and J. Vandewalle",
year = "1991",
title = "The Total Least Squares Problem: Computational Aspects
and Analysis",
publisher = "SIAM",
address = "Philadelphia",
kwds = "book, la, nla, stat, regr, total least squares, svd"
}
@techreport{vkvd:77,
author = "Van Kats, J. M. and Van der Vorst, H. A.",
year = "1977",
title = "Automatic Monitoring of {L}anczos Schemes for Symmetric or
Skew-Symmetric Generalized Eigenvalue Problems",
number = "TR 7",
institution = "Academische Computer Centre",
address = "Utrecht, The Netherlands",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, Lanczos algorithm, symmetric matrix,
skew-symmetric matrix"
}
@article{vkem:66,
author = "van Kempen, H. P. M.",
year = "1966",
title = "On Quadratic Convergence of the Special Cyclic {J}acobi Method",
journal = "Numerische Mathematik",
volume = "9",
pages = "19--22",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Jacobi's method, eig"
}
@unpublished{vloa:72,
author = "Van Loan, C. F.",
year = "1972",
title = "An Algorithm for the Generalized Matrix Eigenvalue
Problem {$Ax=\lambda Bx$} for the Important Case
{$N=2$}",
note = "Appeared as an appendix in Van Loan's
thesis, 1973. Manuscript",
kwds = "nla, geig"
}
@phdthesis{vloa:73,
author = "Van Loan, C. F.",
year = "1973",
title = "Generalized Singular Values with Algorithms and Applications",
school = "University of Michigan",
address = "Ann Arbor, MI",
note = "Cited in \cite{govl:89}.",
kwds = "nla, gsvd"
}
@article{vloa:75,
author = "Van Loan, C. F.",
year = "1975",
title = "A General Matrix Eigenvalue Algorithm",
journal = "SIAM Journal on Numerical Analysis",
volume = "12",
pages = "819-834",
kwds = "math, la, nla, gsvd"
}
@unpublished{vloa:75a,
author = "Van Loan, C. F.",
year = "1975",
title = "Notes on {$e^{At}$}",
note = "Manuscript. Mathematics Department,
University of Manchester, Manchester,
England.",
kwds = "la, nla, matrix exponential, matrix function"
}
@techreport{vloa:75b,
author = "Van Loan, C. F.",
year = "1975",
title = "A Study of the Matrix Exponential",
number = "10",
institution = "Numerical Analysis, University of Manchester",
address = "England",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential"
}
@article{vloa:76,
author = "Van Loan, C. F.",
year = "1976",
title = "Generalizing the Singular Value Decomposition",
journal = "SIAM Journal on Numerical Analysis",
volume = "13",
pages = "76-83",
kwds = "math, la, nla, gsvd"
}
@unpublished{vloa:76a,
author = "Van Loan, C. F.",
year = "1976",
title = "A Bibliography of the Matrix Exponential",
note = "Manuscript. Department of Computer Science, Cornell University.",
kwds = "la, nla, matrix exponential, matrix function"
}
@incollection{vloa:77,
author = "Van Loan, C. F.",
year = "1977",
title = "On the Limitation and Application of the {P}ad{\'e}
Approximation to the Matrix Exponential",
booktitle = "{P}ad{\'e} and Rational Approximation",
editor = "E. B. Saff and R. S. Varga",
publisher = "Academic Press",
address = "New York",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential, Pade approximation"
}
@article{vloa:77a,
author = "Van Loan, C. F.",
year = "1977",
title = "The Sensitivity of the Matrix Exponential",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "14",
pages = "971--981",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, matrix function, matrix exponential"
}
@article{vloa:78,
author = "Van Loan, C. F.",
year = "1978",
title = "Computing Integrals Involving the Matrix Exponential",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-23",
pages = "395--404",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential"
}
@article{vloa:78a,
author = "Van Loan, C. F.",
year = "1978",
title = "A Note on the Evaluation of Matrix Polynomials",
journal = "{IEEE} Transactions on Automatic Control",
volume = "AC-24",
pages = "320--321",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix polynomial"
}
@incollection{vloa:82,
author = "Van Loan, C. F.",
year = "1982",
title = "Using the {H}essenberg Decomposition in Control Theory",
booktitle = "Algorithms and Theory in Filtering and Control",
editor = "D. C. Sorensen and R. J. Wets",
series = "Mathematical Programming Study",
Number = 18,
publisher = "North-Holland",
address = "Amsterdam",
pages = "102--111",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Hessenberg matrix, control"
}
@article{vloa:84,
author = "Van Loan, C. F.",
year = "1984",
title = "A Symplectic Method for Approximating All the Eigenvalues of a
{H}amiltonian Matrix",
journal = "Linear Algebra and its Applications",
volume = "61",
pages = "233--252",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, J-orthogonal matrix, J-symmetric matrix"
}
@article{vloa:85,
author = "Van Loan, C. F.",
year = "1985",
title = "On the Method of Weighting for Equality Constrained
Least Squares",
journal = "SIAM Journal on Numerical Analysis",
volume = "22",
pages = "851--864",
kwds = "nla, lsq, constraints, weights"
}
@article{vloa:85a,
author = "Van Loan, C. F.",
year = "1985",
title = "Computing the {CS} and the Generalized Singular Value
Decompositions",
journal = "Numerische Mathematik",
volume = "479--491",
pages = "479--491",
kwds = "nla, csd, gsvd"
}
@article{vloa:85b,
author = "Van Loan, C. F.",
year = "1985",
title = "How Near is a Stable Matrix to an Unstable Matrix?",
journal = "Contemporary Mathematics",
volume = "47",
pages = "465--477",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, eig, control, stable matrix"
}
@article{vloa:87,
author = "Van Loan, C. F.",
year = "1987",
title = "On Estimating the Condition of Eigenvalues and Eigenvectors",
journal = "Linear Algebra and its Applications",
volume = "88/89",
pages = "715--732",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, condition"
}
@inproceedings{vnes:86,
author = "Van Ness, J. E.",
year = "1986",
title = "Examples of Eigenvalue/vector Use in Electric
Power System Problems",
booktitle = "Large Scale Eigenvalue Problems",
editor = "J. Cullum and R. A. Willoughby",
pages = "181-192",
publisher = "Elsiveir",
address = "Amsterdam",
kwds = "la, eig, sparse, power systems"
}
@article{vree:69,
author = "Van Reeken, A. J.",
year = "1969",
title = "Dealing with {Weely's} Algorithms",
journal = "Communications of the ACM",
pages = "149-150",
kwds = "Weeley's algorithm"
}
@techreport{vant:81,
author = "H. Vantliborgh",
year = "1981",
title = "The Error of Aggregation in Decomposable Systems",
institution = "Philips Research Laboratory,
Brussels, Belgium",
type = "Report",
number = "R 453",
kwds = "nla, Markov chain, nearly uncoupled system, aggregation"
}
@techreport{vara:67,
author = "J. M. Varah",
year = "1967",
title = "The Computation of Bounds for the Invariant Subspaces
of a General Matrix Operator",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS 66",
kwds = "la, nla, eig, pert, invariant subspace, nonsymmetric matrix"
}
@article{vara:68,
author = "J. M. Varah",
year = "1968",
title = "The Calculation of the Eigenvectors of a General Complex Matrix by
Inverse Iteration",
journal = "Mathematics of Computation",
volume = "22",
pages = "785--791",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, inverse iteration"
}
@article{vara:68a,
author = "J. M. Varah",
year = "1968",
title = "Rigorous Machine Bounds for the Eigensystem of a General Complex
Matrix",
journal = "Mathematics of Computation",
volume = "22",
pages = "793--801",
note = "Cited in \cite{govl:89}.",
kwds = "la, nla, pert, rounding error, complex matrix, eig"
}
@article{vara:70,
author = "J. M. Varah",
year = "1970",
title = "Computing Invariant Subspaces of a General Matrix When the
Eigensystem Is Poorly Determined",
journal = "Mathematics of Computation",
volume = "24",
pages = "137--149",
kwds = "la, nla, eig, pert, invariant subspace, nonsymmetric matrix"
}
@article{vara:72,
author = "J. M. Varah",
year = "1972",
title = "On the Solution of Block-Tridiagonal Systems Arising from Certain
Finite-Difference Equations",
journal = "Mathematics of Computation",
volume = "26",
pages = "859--868",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, block tridiagonal matrix, block algorithm"
}
@article{vara:73,
author = "J. M. Varah",
year = "1973",
title = "On the Numerical Solution of Ill-Conditioned Linear Systems with
Applications to Ill-Posed Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "10",
pages = "257--267",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, ill-conditioned problem, condition, regularization,
ill-posed problem"
}
@article{vara:75,
author = "J. M. Varah",
year = "1975",
title = "A Lower Bound for the Smallest Singular Value of a Matrix",
journal = "Linear Algebra and Its Applications",
volume = "11",
pages = "1--2",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "na, condition, svd, pert"
}
@article{vara:79,
author = "J. M. Varah",
year = "1979",
title = "A Practical Examination of some Numerical Methods for Linear
Discrete Ill-Posed Problems",
journal = "SIAM Review",
volume = "21",
pages = "100--111",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, ill-posed problem, regularization"
}
@article{vara:79a,
author = "J. M. Varah",
year = "1979",
title = "On the Separation of Two Matrices",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "16",
pages = "216--222",
note = "Cited in \cite{govl:89}.",
kwds = "la, pert, invariant subspace, eig"
}
@article{varg:61,
author = "R. S. Varga",
year = "1961",
title = "On Higher-Order Stable Implicit Methods for Solving Parabolic
Partial Differential Equations",
journal = "Journal of Mathematical Physics",
volume = "40",
pages = "220--231",
note = "Cited in \cite{govl:89}.",
kwds = "nla, na, pde, parabolic equation"
}
@book{varg:62,
author = "R. S. Varga",
year = "1962",
title = "Matrix Iterative Analysis",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, nla, iter, linear system, pde"
}
@article{varg:64,
author = "R. S. Varga",
year = "1964",
title = "On Smallest Isolated {Gerschgorin} Disks for Eigenvalues",
journal = "Numerische Mathematik",
volume = "6",
pages = "366--376",
kwds = "la, eig, Gerschgorin's theorem"
}
@article{varg:70b,
author = "R. S. Varga",
year = "1970",
title = "Minimal {G}ershgorin Sets for Partitioned Matrices",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "7",
pages = "493--507",
note = "Cited in \cite{govl:89}.",
kwds = "la, eig, Gerschgorin's theorem, block matrix"
}
@article{varg:73,
author = "R. S. Varga",
year = "1973",
title = "On a Connection between Infima of Norms and Eigenvalues
of Associated Operators",
journal = "Linear Algebra and Its Applications",
volume = "6",
pages = "249--256",
kwds = "la, norm, eig"
}
@article{vale:73,
author = "R. S. Varga and B. W. Levinger",
year = "1973",
title = "On Minimal {Gerschgorin} Sets for Families of Norms",
journal = "Numerische Mathematik",
volume = "20",
pages = "252--256",
kwds = "la, Gerschgorin's theorem, eig, norm"
}
@article{varg:76,
author = "R. S. Varga",
year = "1976",
title = "On Diagonal Dominance Arguments for Bounding {$\|A^{-1}\|$}",
journal = "Linear Algebra and its Applications",
volume = "14",
pages = "211--217",
note = "Cited in \cite{govl:89}.",
kwds = "la, diagonal dominance, condition"
}
-vb- -vc- -vd- -ve-
@article{veyp:80,
author = "P. F. Velleman and M. A. Ypelaar",
year = "1980",
title = "Constructing Regressions with Controlled Features: A Method of
Probing Robust Regression Performance",
journal = "Journal of the American Statistical Association",
kwds = "stat, regr, condition, test matrix, robust estimation"
}
@article{vevk:79,
author = "G. Verghese and Van Dooren, P. and T. Kailath",
year = "1979",
title = "Properties of the System Matrix of a Generalized
State-Space System",
journal = "International Journal on Control",
volume = "30",
pages = "235--243",
kwds = "la, control, transfer function"
}
@article{vett:75,
author = "W. J. Vetter",
year = "1975",
title = "Vector Structures and Solutions of Linear Matrix Equations",
journal = "Linear Algebra and its Applications",
volume = "10",
pages = "181--188",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, vect"
}
-vf- -vg- -vh- -vi-
@article{vill:64,
author = "C. Villegas",
year = "1964",
title = "Confidence Region for a Linear Relation",
journal = "Annals of Mathematical Statistics",
volume = "35",
pages = "780-788",
kwds = "stat, regr, hypothesis testing"
}
-vj- -vk- -vl- -vm- -vn- -vo-
@article{vneu:37,
author = "von Neumann, J.",
year = "1937",
title = "Some Matrix-Inequalities and Metrization of Matrix-Space",
journal = "Tomsk. Univ. Rev.",
volume = "1",
pages = "286-300",
note = "In \cite[v.4, pp.205--219]{vneu:62}.",
kwds = "la, norm, svd"
}
@book{vneu:62,
author = "von Neumann, J.",
year = "1962",
title = "Collected Works, {\rm (A. H. Taub Editor)}",
publisher = "Pergamon",
address = "New York",
kwds = "book, history, von Neumann"
}
@article{vngo:47,
author = "von Neumann, J. and H. H. Goldstine",
year = "1947",
title = "Numerical Inverting of Matrices of High Order",
journal = "Bulletin of the American Mathematical Society",
volume = "53",
pages = "1021--1099",
kwds = "nla, linear system, rounding error"
}
-vp- -vq- -vr- -vs- -vt- -vu- -vv- -vw- -vx- -vy- -vz-
-wa-
@book{wach:66,
author = "E. L. Wachpress",
year = "1966",
title = "Iterative Solution of Elliptic Systems",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, NJ",
note = "Cited in \cite{govl:89}.",
kwds = "book, nla, iter, pde, elliptic equation, linear system"
}
@inproceedings{wacf:88,
author = "D. W. Walker and T. Aldcroft and A. Cisneros and G. Fox and
W. Furmanski",
year = "1988",
title = "{LU} Decomposition of Banded Matrices and the Solution of Linear
Systems on Hypercubes",
booktitle = "The Third Conference on Hypercube Concurrent Computers and
Applications, Vol. {II}, Applications",
editor = "G. Fox",
publisher = "{ACM} Press",
address = "New York",
pages = "1635--1655",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, lud, band matrix, prll, hypercube"
}
@article{walk:88,
author = "H. F. Walker",
year = "1988",
title = "Implementation of the {GMRES} Method Using {H}ouseholder
Transformations",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "9",
pages = "152--163",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, Householder transformation, gmres"
}
@techreport{waks:92,
author = "B. Wald\'en and R. Karlson and J.-G. Sun",
year = "1992",
title = "Optimal BAckward Perturbation Bounds for the
Linear Least Squares Problem",
institution = "Department of Mathematics, Link{\"o}ping University",
type = "Technical Report",
number = "LiTH-MAT-R-1992-06",
kwds = "la, pert, lsq, backward perturbation"
}
@book{wall:48,
author = "H. S. Wall",
year = "1948",
title = "Continued Fractions",
publisher = "Van Nostrand",
address = "New York",
note = "Reprinted by Chelsea, New York, 1967.",
kwds = "book, continued fraction, orthogonal polynomial"
}
@article{wamp:69,
author = "R. H. Wampler",
year = "1969",
title = "An Evaluation of Linear Least Squares Computer Programs",
journal = "Journal of Research of the National Bureau of Standards",
volume = "73B",
pages = "59--90",
kwds = "stat, nla, regr, lsq, rounding error"
}
@article{wamp:70,
author = "R. H. Wampler",
year = "1970",
title = "A Report on the Accuracy of some Widely Used Least Squares
Computer Programs",
journal = "Journal of the American Statistical Association",
volume = "65",
pages = "549--565",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, rounding error, Gram-Schmidt algorithm"
}
@inproceedings{wamp:72,
author = "R. H. Wampler",
year = "1972",
title = "Some Recent Developments in Linear Least Squares Computations",
booktitle = "In Proceedings of the Computer Science and Statistics:
Sixth Annual Symposium on the Interface",
editor = "M.E. Tarter",
publisher = "Academic Press",
address = "Berkeley",
pages = "",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "stat, Gram-Schmidt algorithm, lsq"
}
@article{wamp:79,
author = "R. H. Wampler",
year = "1979",
title = "Solutions to Weighted Least Squares Problems by
Modified {Gram--Schmidt} with Iterative Refinement",
journal = "ACM Transactions on Mathematical Software",
volume = "5",
pages = "457--465",
kwds = "nla, lsq, qrd, Gram-Schmidt algorithm, iterative refinement,
weights"
}
@article{wamp:79a,
author = "R. H. Wampler",
year = "1979",
title = "{L2A} and {L2B}, Weighted Least Squares Solutions by
Modified {Gram--Schmidt} with Iterative Refinement",
journal = "ACM Transactions on Mathematical Software",
volume = "5",
pages = "494--99",
kwds = "nla, lsq, qrd, Gram-Schmidt algorithm, iterative refinement,
weights"
}
@article{wamp:80,
author = "R. H. Wampler",
year = "1980",
title = "Test Procedures and Test Problems for Least Squares
Algorithms",
journal = "Journal of Economics",
volume = "12",
pages = "3--22",
kwds = "nla, lsq, rounding error, test matrix"
}
@article{wang:63,
author = "J.-R. Wang",
year = "1963",
title = "A Gradient Method for Finding the Eigenvalues and
Eigenvectors of a Self-Adjoint Operator",
journal = "Acta Math. Sinica",
volume = "13",
pages = "23--28",
note = "Also in {\it Chinese Math.\/}{\bf 4} (1963) 24--30.",
kwds = "nla, eig, symmetric matrix, sparse"
}
@article{ward:75,
author = "R. C. Ward",
year = "1975",
title = "The Combination Shift {QZ} Algorithm",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "12",
pages = "835--853",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, QZ algorithm"
}
@article{ward:77,
author = "R. C. Ward",
year = "1977",
title = "Numerical Computation of the Matrix Exponential with Accuracy
Estimate",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "14",
pages = "600--614",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential"
}
@article{wagr:78,
author = "R. C. Ward and L. J. Gray",
year = "1978",
title = "Eigensystem Computation for Skew-Symmetric and a Class of
Symmetric Matrices",
journal = "{ACM} Transactions on Mathematical Software",
volume = "4",
pages = "278--285",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, symmetric matrix, skew-symmetric matrix"
}
@article{ward:81,
author = "R. C. Ward",
year = "1981",
title = "Balancing the Generalized Eigenvalue Problem",
journal = "{SIAM} Journal on Scientific and Statistical Computing",
volume = "2",
pages = "141--152",
note = "Cited in \cite{govl:89}.",
kwds = "nla, geig, scaling"
}
@phdthesis{warn:74,
author = "D. D. Warner",
year = "1974",
title = "Hermite Interpolation with Rational Functions",
school = "Mathematics Department, University of California,
La Jolla",
kwds = "na, interpolation"
}
@article{watk:82,
author = "D. S. Watkins",
year = "1982",
title = "Understanding the {QR}~Algorithm",
journal = "SIAM Review",
volume = "24",
pages = "427--440",
kwds = "nla, QR algorithm, eig"
}
@book{watk:91,
author = "D. S. Watkins",
year = "1991",
title = "Fundamentals of Matrix Computations",
publisher = "John Wiley \& Sons",
address = "New York",
kwds = "book, nla"
}
@article{wats:73,
author = "G. A. Watson",
year = "1973",
title = "An Algorithm for the Inversion of Block Matrices of
{T}oeplitz Form",
journal = "Journal of the {ACM}",
volume = "20",
pages = "409--415",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, block algorithm, block Toeplitz matrix"
}
@inproceedings{wats:84,
author = "G. A. Watson",
year = "1984",
title = "The Numerical Solution of Total $\ell_p$ Approximation
Problems",
booktitle = "In Proceedings of the 1983 Dundee Conference on Numerical
Analysis",
editor ="D.F. Griffiths",
publisher = "Springer Verlag",
pages = "72--105",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, Hoelder approximation, robust estimation"
}
@article{wats:88,
author = "G. A. Watson",
year = "1988",
title = "The Smallest Perturbation of a Submatrix which Lowers the Rank of
the Matrix",
journal = "{IMA} Journal of Numerical Analysis",
volume = "8",
pages = "295--304",
note = "Cited in \cite{govl:89}.",
kwds = "na, pert, rank determination, matrix approximation"
}
-wb- -wc- -wd- -we-
@article{wegm:74,
author = "J. Webster and R. Gunst and R. Mason",
year = "1974",
title = "Latent Root Regression Analysis",
journal = "Technometrics",
volume = "16",
pages = "513-522",
kwds = "stat, regr, latent root regression, total least squares, svd, eig"
}
@article{wegm:76,
author = "J. Webster and R. Gunst and R. Mason",
year = "1976",
title = "A Comparison of Least Squares and Latent Root Regression
Estimators",
journal = "Technometrics",
volume = "18",
pages = "75--83",
kwds = "stat, regr, latent root regression, total least squares, svd, eig"
}
@article{wedd:25,
author = "J. H. M. Wedderburn",
year = "1925",
title = "The Absolute Value of the Product of Two Matrices",
journal = "Bulletin of the American Mathematical Society",
volume = "31",
pages = "304-308",
kwds = "math, la"
}
@book{wedd:34,
author = "J. H. M. Wedderburn",
year = "1934",
title = "Lectures on Matrices",
series = "American Mathematical Society Colloquium Publications,
V. XVII",
publisher = "American Mathematical Society",
address = "New York",
kwds = "book, la"
}
@article{wedd:76,
author = "R. W. M. Wedderburn",
year = "1976",
title = "On the Existence and Uniqueness of the Maximum
Likelihood Estimates for Certain Generalized
Linear Models",
journal = "Biometrika",
volume = "63",
pages = "27--32",
kwds = "stat, generalized linear model"
}
@techreport{wedi:69,
author = "P.-{\AA}. Wedin",
year = "1969",
title = "On Pseudoinverses of Perturbed Matrices",
institution = "Department of Computer Science, Lund University",
type = "Technical Report",
number = "",
kwds = "la, pert, ginv"
}
@article{wedi:72,
author = "P.-{\AA}. Wedin",
year = "1972",
title = "Perturbation Bounds in Connection with Singular
Value Decomposition",
journal = "BIT",
volume = "12",
pages = "99-111",
kwds = "la, svd, pert"
}
@techreport{wedi:72a,
author = "P.-{\AA}. Wedin",
year = "1972",
title = "The Non-Linear Least Squares Problem from a Numerical
Point of View. {I} Geometrical Properties",
institution = "Department of Computer Sciences, Lund University",
type = "Technical Report",
number = "",
kwds = "nlop, lsq, nllsq"
}
@article{wedi:73,
author = "P.-{\AA}. Wedin",
year = "1973",
title = "Pertubation Theory for Pseudo-Inverses",
journal = "BIT",
volume = "13",
pages = "217-232",
kwds = "la, pert, ginv"
}
@article{wedi:73a,
author = "P.-{\AA}. Wedin",
year = "1973",
title = "On the Almost Rank Deficient Case of the Least
Squares Problem",
journal = "BIT",
volume = "13",
pages = "344--354",
kwds = "la, lsq, pert, rank determination"
}
@techreport{wedi:74,
author = "P.-{\AA}. Wedin",
year = "1974",
title = "On the {Gauss-Newton} Method for the Nonlinear Least
Squares Problems",
institution = "Institute for Applied Mathematics, Stockholm",
type = "Working Paper",
number = "24",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, Gauss-Newton method"
}
@techreport{wedi:78,
author = "P.-{\AA}. Wedin",
year = "1978",
title = "Perturbations of the Pseudo-Inverse and the Linear Least
Squares Problem Analysed with Suitable Matrix Decompositions",
institution = "Institute of Information Processing, University of Ume\aa",
type = "Technical Report",
number = "UMINF--69.78",
kwds = "la, pert, lsq, ginv"
}
@techreport{wedi:79,
author = "P.-{\AA}. Wedin",
year = "1979",
title = "Notes on the Constrained Linear Least Squares Problem. A New
Approach Based on Generalized Inverses",
institution = "Institute of Information Processing, University of Ume\aa",
type = "Technical Report",
number = "UMINF--75.79",
kwds = "la, nla, lsq, constraints, ginv"
}
@inproceedings{wedi:83,
author = "P.-{\AA}. Wedin",
year = "1983",
title = "On Angles Between Subspaces",
booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
pages = "263-285",
publisher = "Springer",
address = "New York",
kwds = "nla, svd, csd, gsvd, canonical angles, subspace metric"
}
@techreport{wedi:85,
author = "P.-{\AA}. Wedin",
year = "1985",
title = "Perturbation Theory and Condition Numbers for Generalized
and Constrained Linear Least Squares Problems",
institution = "Institute of Information Processing, University of Ume\aa",
type = "Technical Report",
number = "UMINF--125.85",
kwds = "la, pert, lsq, constraints, condition"
}
@techreport{wedi:87,
author = "P.-{\AA}. Wedin",
year = "1987",
title = "Perturbation Theory and Condition Numbers for Generalized
and Constrained Least Squares Problems",
institution = "Institute of Information Processing, University of
Ume\aa",
type = "Technical Report",
number = "S-901-87",
kwds = "la, lsq, ginv, constraints, pert, condition"
}
@unpublished{wedi:91,
author = "P.-{\AA}. Wedin",
year = "1991",
title = "Some Thoughts on Perturbation Bounds for the Polar
Decomposition and Other Perturbation Problems in
Linear Algebra",
note = "Manuscript, Institute of Information Processing, University of
Ume\aa",
kwds = "la, pert, polar decomposition"
}
@article{wei:90,
author = "M. Wei",
year = "1990",
title = "Perturbation of the Least Squares Problem",
journal = "Linear Algebra and Its Applications",
volume = "141",
pages = "177--182",
kwds = "la, pert, lsq"
}
@article{weie:1868,
author = "K. Weierstrass",
year = "1868",
title = " {Zur Theorie der bilinearen und quadratischen Formen}",
journal = "Monatshefte Akadamie Wissenshaften Berlin",
volume = "",
pages = "310--38",
kwds = "la, geig, Weierstrass form"
}
@article{wein:60,
author = "H. F. Weinberger",
year = "1960",
title = "Error Bounds in the {Rayleigh--Ritz} Approximation of
Eigenvectors",
journal = "Journal of Research of the National Bureau of Standards",
volume = "64B",
pages = "217--225",
kwds = "la, eig, pert, Rayleigh-Ritz method, symmetric matrix"
}
@book{wein:74,
author = "H. F. Weinberger",
year = "1974",
title = "Variational Methods for Eigenvalue Approximation",
publisher = "Society for Industrial and Applied Mathematics",
address = "Philadelphia",
note = "Cited in \cite{parl:80}.",
kwds = "book, la, eig, pert, symmetric matrix"
}
@article{wwws:86,
author = "N. Weis and G. W. Wasilkowski and H. Wo\'zniakowski
and M. Shub",
year = "1986",
title = "Average Condition Number for Solving Linear Equations",
journal = "Linear Algebra and Its Applications",
volume = "83",
pages = "79--102",
kwds = "nla, condition, pert, linear system"
}
@book{weis:80,
author = "S. Weisberg",
year = "1980",
title = "Applied Linear Regression",
publisher = "John Wiley",
address = "New York",
kwds = "book, stat, regr"
}
@article{welf:62,
author = "B. P. Welford",
year = "1962",
title = "Note on a Method for Calculating Corrected Sums of Squares and
Products",
journal = "Technometrics",
volume = "4",
pages = "419-420",
kwds = "stat, standard deviation, variance, updating"
}
@book{weso:76,
author = "G. O. Wesolowsky",
year = "1976",
title = "Multiple Regression and Analysis of Variance",
publisher = "John Wiley and Sons",
address = "New York",
kwds = "book, stat, regr"
}
@article{west:79,
author = "D. H. D. West",
year = "1979",
title = "Updating Means and Variance Estimates: an Improved Method",
journal = "Communications of the ACM",
volume = "22",
pages = "532-535",
kwds = "mean, standard deviation, variance, updating"
}
@article{weyl:12,
author = "H. Weyl",
year = "1912",
title = " {Das asymptotische Verteilungsgesetz der Eigenwert
linearer partieller Differentialgleichungen (mit
einer Anwendung auf der Theorie der Hohlraumstrahlung)}",
journal = "Mathematische Annalen",
volume = "71",
pages = "441--479",
kwds = "la, pde, eig, pert, symmetric matrix"
}
@article{weyl:49,
author = "H. Weyl",
year = "1949",
title = "Inequalities between the Two Kinds of Eigenvalues of a
Linear Transformation",
journal = "Proceedings of the National Academy of Sciences",
volume = "35",
pages = "408--411",
kwds = "la, eig, svd"
}
-wf- -wg- -wh-
@book{whro:44,
author = "E. Whittaker and G. Robinson",
year = "1944",
title = "The Calculus of Observations",
publisher = "Blackie and Son",
address = "London",
note = "4th Edition",
kwds = "book, stat, regr, lsq"
}
-wi-
@inproceedings{widl:72,
author = "O. B. Widlund",
year = "1972",
title = "On the Use of Fast Methods for Separable Finite Difference
Equations for the Solution of General Elliptic Problems",
booktitle = "Sparse Matrices and Their Applications",
editor = "D. J. Rose and R. A. Willoughby",
pages = "121--134",
publisher = "Plenum Press",
address = "New York",
kwds = "nla, pde, fast algorithm, elliptic pde"
}
@article{widl:78,
author = "O. Widlund",
year = "1978",
title = "A {L}anczos Method for a Class of Nonsymmetric Systems of Linear
Equations",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "15",
pages = "801--812",
note = "Cited in \cite{govl:89}.",
kwds = "nla, Lanczos algorithm, linear system, nonsymmetric matrix"
}
@article{wiel:55,
author = "H. Wielandt",
year = "1955",
title = "An Extremum Property of Sums of Eigenvalues",
journal = "Proceedings of the American Mathematical Society",
volume = "6",
pages = "106--110",
kwds = "la, eig, pert"
}
@article{wiel:73,
author = "H. Wielandt",
year = "1973",
title = "On the Eigenvalues of {$A+B$} and {$AB$}",
journal = "Journal of Research of the National Bureau of Standards",
volume = "77B",
pages = "61--63",
note = "A minor revision of NBS Report No.~1367, 1951.",
kwds = "la, eig, pert"
}
@article{wien:22,
author = "N. Wiener",
year = "1922",
title = "Limit in Terms of Continuous Transformations",
journal = "Bulletin de le Soci\'et\'e Math\'ematique de France",
volume = "50",
pages = "119-134",
kwds = "functional analysis, Banach space"
}
@article{wilk:77,
author = "G. N. Wilkinson",
year = "1977",
title = "On Resolving the Controversy in Statistical Inference",
journal = "Journal of the Royal Statistical Society, Series B",
volume = "39",
pages = "119--171",
kwds = "stat, hypothesis testing"
}
@article{wilk:59?,
author = "J. H. Wilkinson",
year = "1959?",
title = "The Calculation of Eigenvectors by the Method of {Lanczos}",
journal = "Computer Journal",
volume = "",
pages = "148--152",
kwds = "nla, eig, Lanczos algorithm, symmetric matrix, sparse"
}
@article{wilk:59,
author = "J. H. Wilkinson",
year = "1959",
title = "The Evaluation of the Zeros of Ill-Conditioned Polynomials.
{Part~I}",
journal = "Numerische Mathematik",
volume = "1",
pages = "150--166",
kwds = "nlop, polynomial, ill-conditioned problem"
}
@article{wilk:60,
author = "J. H. Wilkinson",
year = "1960",
title = "Error Analysis of Floating-Point Computation",
journal = "Numerische Mathematik",
volume = "2",
pages = "319--340",
kwds = "na, computer arithmetic"
}
@article{wilk:61,
author = "J. H. Wilkinson",
year = "1961",
title = "Error Analysis of Direct Methods of Matrix Inversion",
journal = "Journal of the ACM",
volume = "8",
pages = "281-330",
kwds = "nla, rounding error, lud"
}
@article{wilk:62,
author = "J. H. Wilkinson",
year = "1962",
title = "Note on the Quadratic Convergence of the Cyclic
{Jacobi} Process",
journal = "Numerische Mathematik",
volume = "4",
pages = "296--300",
kwds = "nla, eig, Jacobi's method, symmetric matrix"
}
@article{wilk:62a,
author = "J. H. Wilkinson",
year = "1962",
title = "Householder's Method for Symmetric Matrices",
journal = "Numerische Mathematik",
volume = "4",
pages = "354--361",
note = "Cite in \cite[p.226]{wire:71}.",
kwds = "nla, eig, tridiagonal matrix, Householder transformation,
software"
}
@book{wilk:63,
author = "J. H. Wilkinson",
year = "1963",
title = "Rounding Errors in Algebraic Processes",
publisher = "Prentice-Hall",
address = "Englewood Cliffs, New Jersey",
kwds = "book, math, na, nla, nlop, rounding error, lud"
}
@book{wilk:65,
author = "J. H. Wilkinson",
year = "1965",
title = "The Algebraic Eigenvalue Problem",
publisher = "Clarendon Press",
address = "Oxford, England",
kwds = "book, math, na, nla, eig, rounding error"
}
@incollection{wilk:65a,
author = "J. H. Wilkinson",
year = "1965",
title = "Error Analysis of Transformations Based on the Use of Matrices
of the Form {$I-2xx^{\rm H}$}",
booktitle = "Error in Digital Computation",
editor = "L. B. Rall",
publisher = "John Wiley",
address = "New York",
pages = "77-101",
kwds = "math, rounding error, Householder transformation"
}
@article{wilk:65b,
author = "J. H. Wilkinson",
year = "1965",
title = "Convergence of the {LR}, {QR}, and Related Algorithms",
journal = "Computer Journal",
volume = "8",
pages = "77--84",
kwds = "nla, eig, QR algorithm, LR algorithm"
}
@techreport{wilk:67,
author = "J. H. Wilkinson",
year = "1967",
title = "Two Algorithms Based on Successive Linear Interpolation",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "CS~60",
kwds = "nlop, secant method"
}
@article{wilk:68,
author = "J. H. Wilkinson",
year = "1968",
title = "Global Convergence of Tridiagonal {QR}~Algorithm with
Origin Shifts",
journal = "Linear Algebra and Its Applications",
volume = "1",
pages = "409--420",
kwds = "nla, QR algorithm, eig"
}
@article{wilk:68a,
author = "J. H. Wilkinson",
year = "1968",
title = "Almost Diagonal Matrices with Multiple or Close Eigenvalues",
journal = "Linear Algebra and its Applications",
volume = "1",
pages = "1--12",
note = "Cited in \cite{govl:89}.",
kwds = "nla, eig, pert, diagonal matrix, multiple eigenvalue"
}
@inproceedings{wilk:68b,
author = "J. H. Wilkinson",
year = "1968",
title = "A Priori Error Analysis of Algebraic Processes",
booktitle = "Proceedings International Congress Math.
({M}oscow: {I}zdat. {M}ir)",
pages = "629--639",
note = "Cited in \cite{govl:89}.",
kwds = "na, rounding error"
}
@book{wire:71,
author = "J. H. Wilkinson and C. Reinsch",
year = "1971",
title = "Handbook for Automatic Computation. Vol.~II Linear Algebra",
publisher = "Springer",
address = "New York",
kwds = "book, nla, software, eig, linear system"
}
@article{wilk:71a,
author = "J. H. Wilkinson",
year = "1971",
title = "Modern Error Analysis",
journal = "SIAM Review",
volume = "13",
pages = "548-568",
kwds = "na, rounding error, history"
}
@article{wilk:72,
author = "J. H. Wilkinson",
year = "1972",
title = "Note on Matrices with a Very Ill-Conditioned Eigenproblem",
journal = "Numerische Mathematik",
volume = "19",
pages = "176--178",
kwds = "la, nla, eig, pert, backward perturbation,
ill-conditioned problem"
}
@incollection{wilk:77,
author = "J. H. Wilkinson",
year = "1977",
title = "Some Recent Advances in Numerical Linear Algebra",
booktitle = "The State of the Art in Numerical Analysis",
editor = "D. A. H. Jacobs",
publisher = "Academic Press",
address = "New York",
pages = "1--53",
note = "Cited in \cite{govl:89}.",
kwds = "nla"
}
@techreport{wilk:77a,
author = "J. H. Wilkinson",
year = "1977",
title = "The Use of Single Precision-Residuals in the Solution of
Linear Systems",
institution = "NPL",
type = "unpublished report",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, iterative refinement, rounding error"
}
@incollection{wilk:78,
author = "J. H. Wilkinson",
year = "1978",
title = "Linear Differential Equations and {K}ronecker's Canonical Form",
booktitle = "Recent Advances in Numerical Analysis",
editor = "de Boor, C. and G. H. Golub",
publisher = "Academic Press",
address = "New York",
pages = "231--265",
note = "Cited in \cite{govl:89}.",
kwds = "na, nla, ode, Kronecker form"
}
@article{wilk:79,
author = "J. H. Wilkinson",
year = "1979",
title = "{Kronecker's} Canonical Form and the {QZ}~Algorithm",
journal = "Linear Algebra and Its Applications",
volume = "28",
pages = "285--303",
kwds = "la, geig, pert, Kronecker form, QZ algorithm"
}
@techreport{wilk:79a,
author = "J. H. Wilkinson",
year = "1979",
title = "Note on the Practical Significance of the {Drazin} Inverse",
institution = "Computer Science Department, Stanford University",
type = "Technical Report",
number = "STAN-CS-79-736",
kwds = "la, ginv, Drazin generalized inverse"
}
@article{wilk:84,
author = "J. H. Wilkinson",
year = "1984",
title = "On Neighboring Matrices with Quadratic Elementary Divisors",
journal = "Numerische Mathematik",
volume = "44",
pages = "1--21",
note = "Cited in \cite{govl:89}.",
kwds = "la, eig, multiple eigenvalue, pert"
}
@techreport{will:68,
author = "R. A. Willoughby",
year = "1968",
title = "Sparse Matrix Proceedings",
institution = "IBM Research, Yorktown Heights.",
type = "Report",
number = "RA1",
kwds = "nla, sparse"
}
@article{wizi:72,
author = "H. Wimmer and A. D. Ziebur",
year = "1972",
title = "Solving the Matrix Equation {$\sum f_{p}(A)Xg_{p}(A)$}",
journal = "{SIAM} Review",
volume = "14",
pages = "318--323",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix equation"
}
@article{wino:68,
author = "S. Winograd",
year = "1968",
title = "A New Algorithm for Inner Product",
journal = "{IEEE} Transactions on Computers",
volume = "C-17",
pages = "693--694",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inner product, fast algorithm"
}
@phdthesis{witt:34,
author = "H. Wittmeyer",
year = "1934",
title = "{Einflu\ss\ der \"Anderung einer Matrix auf der L\"osung
des zugeh\"origen Gleichungssystems, sowie auf die
charakteristischen Zahlen und die Eigenvektoren}",
school = "Technische Hochschule zu Darmstadt",
kwds = "nla, pert, eig, linear system"
}
@article{witt:36,
author = "H. Wittmeyer",
year = "1936",
title = "{Einflu\ss\ der \"Anderung einer Matrix auf der L\"osung
des zugeh\"origen Gleichungssystems, sowie auf die
charakteristischen Zahlen und die Eigenvektoren}",
journal = " {Zeitschrift f\"ur angewandte Mathematik und Mechanik}",
volume = "16",
pages = "287--300",
kwds = "la, pert, eig, linear system"
}
-wj- -wk- -wl- -wm- -wn- -wo-
@article{wolf:59,
author = "P. Wolfe",
year = "1959",
title = "The Secant Method for Simultaneous Nonlinear Equations",
journal = "Communications of the ACM",
volume = "12?",
pages = "12--13",
kwds = "nlop, secant method"
}
@article{wolf:72,
author = "P. Wolfe",
year = "1972",
title = "A New Algorithm for Optimization",
journal = "Mathematical Programming",
volume = "3",
pages = "124--128",
note = "Published under the nom de plume Anonymous.",
kwds = "nlop, spoof, separable Hilbert iterative technique"
}
@article{wool:1868,
author = "W. S. B. Woolhouse",
year = "1868",
title = "On General Numerical Solution",
journal = "Proceeding of the London Mathematical Society",
volume = "2",
pages = "75--84",
kwds = "nlop, polynomial"
}
@article{woss:32,
author = "H. Woods and H. H. Steinour and H. R. Starke",
year = "1932",
title = "Effect of Composition of Portland Cement on Heat Evolved during
Hardening",
journal = "Industrial and Engineering Chemistry",
volume = "24",
pages = "1207-1214",
kwds = "stat, regr, Hald data"
}
@article{wosn:80,
author = "H. Wozniakowski",
year = "1980",
title = "Roundoff Error Analysis of a New Class of Conjugate Gradient
Algorithms",
journal = "Linear Algebra and its Applications",
volume = "29",
pages = "507--529",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, rounding error"
}
-wp- -wq- -wr-
@article{wrag:73,
author = "A. Wragg",
year = "1973",
title = "Computation of the Exponential of a Matrix {I}: Theoretical
Considerations",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "11",
pages = "369--375",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential"
}
@article{wrag:75,
author = "A. Wragg",
year = "1975",
title = "Computation of the Exponential of a Matrix {II}: Practical
Considerations",
journal = "Journal of the Institute of Mathematics and its Applications",
volume = "15",
pages = "273--278",
note = "Cited in \cite{govl:89}.",
kwds = "nla, matrix function, matrix exponential"
}
@article{wrho:85,
author = "S. J. Wright and J. N. Holt",
year = "1985",
title = "Algorithms for Nonlinear Least Squares with Linear Inequality
Constraints",
journal = "SIAM Journal on Scientific and Statistical Computing",
volume = "6",
pages = "1033--1048",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nlop, lsq, nllsq, constraints"
}
-ws- -wt- -wu- -wv- -ww- -wx- -wy- -wz-
-xa- -xb- -xc- -xd- -xe- -xf- -xg- -xh- -xi- -xj- -xk- -xl- -xm-
-xn- -xo- -xp- -xq- -xr- -xs- -xt- -xu-
@unpublished{xuka:90,
author = "G. Xu and T. Kailath",
year = "1990",
title = "Fast Signal-subspace Decompsotion\,---\,{Part I}:
{Ideal} Covariance Matrices",
note = "Manuscript submitted to ASSP. Information Systems
Laboratory, Stanford University",
kwds = "nla, stat, Lanczos algorithm, rank determination"
}
@unpublished{xuka:90a,
author = "G. Xu and T. Kailath",
year = "1990",
title = "Fast Signal-subspace Decompsotion\,---\,{Part II}:
{Sample} Covariance Matrices",
note = "Manuscript submitted to ASSP. Information Systems
Laboratory, Stanford University",
kwds = "nla, stat, Lanczos algorithm, rank determination"
}
-xv- -xw- -xx- -xy- -xz-
-ya-
@article{yama:80,
author = "T. Yamamoto",
year = "1980",
title = "Error Bounds for Computed Eigenvalues and Eigenvectors",
journal = "Numerische Mathematik",
volume = "34",
pages = "189--199",
kwds = "la, nla, eig, pert"
}
-yb- -yc- -yd- -ye-
@article{yetl:87,
author = "Pen-Chung Yew and Niau-Feng Txeng and D. H. Lawrie",
year = "1987",
title = "Distributing Hot-Spot Addressing in Large Scale
Multiprocessors",
journal = "IEEE Transactions on Computers",
volume = "C-36",
pages = "338-395",
kwds = "prll, shared memory, communication, contention"
}
-yf- -yg- -yh- -yi- -yj- -yk- -yl- -ym- -yn- -yo-
@article{yohe:79,
author = "J. M. Yohe",
year = "1979",
title = "Software for Interval Arithmetic: A Reasonable Portable Package",
journal = "{ACM} Transactions on Mathematical Software",
volume = "5",
pages = "50--63",
note = "Cited in \cite{govl:89}.",
kwds = "na, interval arithmetic, software"
}
@article{youn:70,
author = "D. M. Young",
year = "1970",
title = "Convergence Properties of the Symmetric and Unsymmetric
Over-Relaxation Methods",
journal = "Mathematics of Computation",
volume = "24",
pages = "793--807",
note = "Cited in \cite{govl:89}.",
kwds = "nla, linear system, relaxation, nonsymmetric matrix"
}
@book{youn:71,
author = "D. M. Young",
year = "1971",
title = "Iterative Solution of Large Linear Systems",
publisher = "Academic Press",
address = "New York",
kwds = "book, nla, iter, linear system"
}
@article{youn:72,
author = "D. M. Young",
year = "1972",
title = "Generalization of Property~{$A$} and Consistent Ordering",
journal = "{SIAM} Journal on Numerical Analysis",
volume = "9",
pages = "454--463",
note = "Cited in \cite{govl:89}.",
kwds = "nla, relaxation"
}
@article{yoje:80,
author = "D. M. Young and K. C. Jea",
year = "1980",
title = "Generalized Conjugate Gradient Acceleration of Nonsymmetrizable
Iterative Methods",
journal = "Linear Algebra and its Applications",
volume = "34",
pages = "159--194",
note = "Cited in \cite{govl:89}.",
kwds = "nla, conjugate gradients, iter"
}
@article{yocr:71,
author = "E. A. Youngs and E. M. Cramer",
year = "1971",
title = "Some Results Relevant to Choice of Sum and Sum-of-Product
Algorithms",
journal = "Technometrics",
volume = "13",
pages = "657-665",
kwds = "stat, mean, standard deviation, variance, updating"
}
-yp- -yq- -yr- -ys- -yt- -yu- -yv- -yw- -yx- -yy- -yz-
-za-
@phdthesis{zarl:76,
author = "R. L. Zarling",
year = "1976",
title = "Numerical Solution of Nearly Decomposable Queuing Networks",
school = "Department of Compter Science, University of North Carolina,
Chapel Hill",
kwds = "nla, Markov chain, nearly uncoupled system, aggregation"
}
@article{zass:64,
author = "H. Zassenhaus",
year = "1964",
title = "`{Angles} of Inclination' in Correllation Theory",
journal = "American Mathematical Monthly",
volume = "71",
pages = "218-219",
kwds = "math, stat, canonical correlation, gsvd, canonical angles"
}
-zb- -zc- -zd- -ze- -zf- -zg- -zh-
@article{zhha:90,
author = "H. Zha and P. C. Hansen",
year = "1989",
title = "Regularization and the General {Gauss--Markov} Linear Model",
journal = "Mathematics of Computation",
volume = "55",
pages = "613--624",
kwds = "nla, regr, regularization"
}
@article{zha:91,
author = "H. Zha",
year = "1991",
title = "The Restricted Singular Value Decomposition
of Matrix Triplets",
journal = "SIAM Journal on Matrix Analysis and Applciations",
volume = "12",
pages = "172--194",
kwds = "nla, geig"
}
@article{zha:91a,
author = "H. Zha",
year = "1991",
title = "Implicit ${QR}$~Factorization of a Product of
Three Matrices",
journal = "BIT",
volume = "31",
pages = "375--379",
kwds = "nla, qrd"
}
@article{zha:91b,
author = "H. Zha",
year = "1991",
title = "A Two-Way Chasing Scheme for Reducing a Symmetric
Arrowhead Matrix to Tridiagonal Form",
journal = "Linear Algebra and Its Applications",
volume = "?",
pages = "?",
note = "To appear.",
kwds = "nla, eig, arrowhead matrix, tridiagonal matrix"
}
@unpublished{zha:91,
author = "H. Zha",
year = "1991",
title = "Adjusting the Diagonal Elements of a Symmetric Matrix
by Orthogonal Similarity Transformation",
note = "Manuscript, Scientific Computing and Computational Mathematics,
Stanford University.",
kwds = "nla, plane rotation"
}
@article{zhan:86,
author = "Z. Zhang",
year = "1986",
title = "On the Perturbation of the Eigenvalues of a Non-Defective
Matrix",
journal = "Math. Numer. Sinica",
volume = "6",
pages = "106--108",
note = "In Chinese.",
kwds = "la, pert, eig, diagonalizable matrix"
}
-zi-
@article{ziel:74,
author = "G. Zielke",
year = "1974",
title = "{Testmatrixen mit maximaler Konditionsxahl}",
journal = "Computing",
volume = "13",
pages = "33--54",
kwds = "nla, condition, test matrix"
}
@article{ziel:86,
author = "G. Zielke",
year = "1986",
title = "Report on Test Matrices for Generalixed Inverses",
journal = "Computing",
volume = "36",
pages = "105--162",
kwds = "nla, ginv, test matrix"
}
@article{ziel:88,
author = "G. Zielke",
year = "1988",
title = "Some Remarks on Matrix Norms, Condition Numbers,
and Error Estimates for Linear Equations",
journal = "Linear Algebra and Its Applications",
volume = "41",
pages = "29--41",
kwds = "la, norm, condition, linear system"
}
-zj- -zk- -zl-
@techreport{zlni:79,
author = "Z. Zlatev and H. Nielsen",
year = "1979",
title = "{LLSS01} - A {Fortran} Subroutine for Solving Least Squares
Problems ({User's} Guide)",
institution = "Institute of Numerical Analysis, Technical University of
Denmark, Lyngby, Denmark",
type = "Technical Report",
number = "79-07",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, software"
}
@article{zlat:82,
author = "Z. Zlatev",
year = "1982",
title = "Comparison of Two Pivotal Strategies in Sparse Plane Rotations",
journal = " Comput. Math. Appl.",
volume = "8",
pages = "119--135",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, sparse, plane rotation, pivoting"
}
@article{zlni:88,
author = "Z. Zlatev and H. Nielsen",
year = "1988",
title = "Solving Large and Sparse Linear Least-Squares Problems by
Conjugate Gradient Algorithms",
journal = "Comput. Math. Applic.",
volume = "15",
pages = "185--202",
note = "Cited in {\AA ke Bj\"orck's} bibliography on least squares,
which is available by anonymous ftp from {\tt math.liu.se} in
{\tt pub/references}.",
kwds = "nla, lsq, conjugate gradients"
}
-zm- -zn- -zo-
@article{zoha:69,
author = "S. Zohar",
year = "1969",
title = "{T}oeplitz Matrix Inversion: The Algorithm of {W}.{F}. {T}rench",
Journal = {"Journal of the {ACM}"},
volume = "16",
pages = "592--601",
note = "Cited in \cite{govl:89}.",
kwds = "nla, inverse matrix, Toeplitz matrix"
}
-zp- -zq- -zr-
-zs- -zt- -zu- -zv- -zw- -zz- -zy- -zz-
@unpublished{altkeys,
author = "Zzzzz, Rip van",
year = "1991",
title = "Alternate Key Words",
kwds = "analysis of variance (try anova),
computer science (try cs),
condition (also try diagnostic; pert),
CS decomposition (try csd),
downdating (try updating),
Eckart-Young theorem (try Schmidt-Mirsky theorem),
eigenvalue problems (try eig),
equilibration (try scaling),
errors in variables (try eriv),
floating point (try computer arithmetic; rounding error),
gap (also try subspace metric),
generalized eigenvalue problems (try geig),
generalized inverse (try ginv),
generalized singular value decomposition (try gsvd),
Gauss-Seidel (try relaxation),
Givens rotation (try plane rotation),
Hermitian matrix (try symmetric matrix),
Hamiltonian matrix (try J-symmetric matrix),
iterative method (try iter),
ill-posed (try regularization),
Jacobi iteration (also try relaxation),
lambda matrix (also try matrix polynomial; geig),
least squares (try lsq; also regr),
linear algebra (try la),
LU decomposition (try lud),
mathematics (try math),
matrix pencil (also try geig),
matrix polynomial (also try lambda matrix; geig),
non-Hermitian matrix (try nonsymmetric matrix),
nonlinear equations and optimixation (try nlop),
nonlinear least squares (try nllsq),
numerical analysis (try na),
numerical linear algebra (try nla),
numerical range (try field of values),
orthogonalization (also try Gram-Schmidt algorithm),
pseudo-inverse (try ginv),
parallel computation (try prll),
perturbation theory (try pert),
positive definite matrix (also try Cholesky decomposition),
QR decomposition (try qrd),
regression (try regr; lsq),
rounding error (also try computer arithmetic),
singular value decomposition (try svd),
simultaneous iteration (try subspace iteration),
stochastic matrix (also try Markov Chain),
sor (try relaxation),
sparse (also try iter; conjugate gradients; etc.),
stability (also try rounding error; pert; condition),
statistics (try stat),
symplectic matrix (try J-orthogonal matrix),
unitary matrix (try orthogonal matrix)"
}