%{AMS}
@String{AMSTrans = "American Mathematical Society Translations" }
@String{AMSTrans = "Amer. Math. Soc. Transl." }
@String{BullAMS = "Bulletin of the American Mathematical Society" }
@String{BullAMS = "Bull. Amer. Math. Soc." }
@String{ProcAMS = "Proceedings of the American Mathematical Society" }
@String{ProcAMS = "Proc. Amer. Math. Soc." }
@String{TransAMS = "Transactions of the American Mathematical Society" }
@String{TransAMS = "Trans. Amer. Math. Soc." }
%ACM
@String{CACM = "Communications of the {ACM}" }
@String{CACM = "Comm. {ACM}" }
@String{CompServ = "{ACM} Computing Surveys" }
@String{CompServ = "Comput. Surveys" }
@String{JACM = "Journal of the {ACM}" }
@String{JACM = "J. Assoc. Comput. Mach." }
@String{ACMMathSoft = "{ACM} Transactions on Mathematical Software" }
@String{ACMMathSoft = "{ACM} Trans. Math. Software" }
@String{SIGNUM = "{ACM} {SIGNUM} Newsletter" }
@String{SIGNUM = "{ACM} {SIGNUM} Newslett." }
@String{AmerSocio = "American Journal of Sociology" }
@String{AmerSocio = "Amer. J. Sociology" } % didn't find in AMS MR
@String{AmerStatAssoc = "Journal of the American Statistical Association" }
@String{AmerStatAssoc = "J. Amer. Statist. Assoc." }
@String{ApplMathComp = "Applied Mathematics and Computation" }
@String{ApplMathComp = "Appl. Math. Comput." }
@String{AmerMathMonthly = "American Mathematical Monthly" }
@String{AmerMathMonthly = "Amer. Math. Monthly" }
@String{BIT = "{BIT}" }
@String{BIT = "{BIT}" }
@String{BritStatPsych = "British Journal of Mathematical and Statistical
Psychology" }
@String{BritStatPsych = "Brit. J. Math. Statist. Psych." }
@String{CanMathBull = "Canadian Mathematical Bulletin" }
@String{CanMathBull = "Canad. Math. Bull." }
@String{CompApplMath = "Journal of Computational and Applied Mathematics" }
@String{CompApplMath = "J. Comput. Appl. Math." }
@String{CompPhys = "Journal of Computational Physics" }
@String{CompPhys = "J. Comput. Phys." }
@String{CompStruct = "Computers and Structures" }
@String{CompStruct = "Comput. \& Structures" }
@String{CompJour = "The Computer Journal" }
@String{CompJour = "Comput. J." }
@String{CompSysSci = "Journal of Computer and System Sciences" }
@String{CompSysSci = "J. Comput. System Sci." }
@String{Computing = "Computing" }
@String{Computing = "Computing" }
@String{ContempMath = "Contemporary Mathematics" }
@String{ContempMath = "Contemp. Math." }
@String{Crelle = "Crelle's Journal" }
@String{Crelle = "Crelle's J." } % didn't find in AMS MR.
@String{GiornaleMath = "Giornale di Mathematiche" }
@String{GiornaleMath = "Giorn. Mat." } % didn't find in AMS MR., ibid.
%IEEE
@String{Computer = "{IEEE} Computer" }
@String{Computer = "{IEEE} Computer" }
@String{IEEETransComp = "{IEEE} Transactions on Computers" }
@String{IEEETransComp = "{IEEE} Trans. Comput." }
@String{IEEETransAC = "{IEEE} Transactions on Automatic Control" }
@String{IEEETransAC = "{IEEE} Trans. Automat. Control" }
@String{IEEESpec = "{IEEE} Spectrum" }
@String{IEEESpec = "{IEEE} Spectrum" } % didn't find in AMS MR
@String{ProcIEEE = "Proceedings of the {IEEE}" }
@String{ProcIEEE = "Proc. {IEEE}" } % didn't find in AMS MR
@String{IEEETransAeroElec = "{IEEE} Transactions on Aerospace and Electronic
Systems" }
@String{IEEETransAeroElec = "{IEEE} Trans. Aerospace Electron. Systems" }
@String{IMANumerAna = "{IMA} Journal of Numerical Analysis" }
@String{IMANumerAna = "{IMA} J. Numer. Anal." }
@String{InfProcLet = "Information Processing Letters" }
@String{InfProcLet = "Inform. Process. Lett." }
@String{InstMathApp = "Journal of the Institute of Mathematics and
its Applications" }
@String{InstMathApp = "J. Inst. Math. Appl." }
@String{IntControl = "International Journal of Control" }
@String{IntControl = "Internat. J. Control" }
@String{IntNumerEng = "International Journal for Numerical Methods in
Engineering" }
@String{IntNumerEng = "Internat. J. Numer. Methods Engrg." }
@String{IntSuper = "International Journal of Supercomputing Applications" }
@String{IntSuper = "Internat. J. Supercomputing Applic." } % didn't find
@String{Kibernetika = "Kibernetika" }
@String{Kibernetika = "Kibernetika" }
@String{JResNatBurStand = "Journal of Research of the National Bureau
of Standards" }
@String{JResNatBurStand = "J. Res. Nat. Bur. Standards" }
@String{LinAlgApp = "Linear Algebra and its Applications" }
@String{LinAlgApp = "Linear Algebra Appl." }
@String{MathAnaAppl = "Journal of Mathematical Analysis and Applications" }
@String{MathAnaAppl = "J. Math. Anal. Appl." }
@String{MathAnnalen = "Mathematische Annalen" }
@String{MathAnnalen = "Math. Ann." }
@String{MathPhys = "Journal of Mathematical Physics" }
@String{MathPhys = "J. Math. Phys." }
@String{MathComp = "Mathematics of Computation" }
@String{MathComp = "Math. Comp." }
@String{MathScand = "Mathematica Scandinavica" }
@String{MathScand = "Math. Scand." }
@String{TablesAidsComp = "Mathematical Tables and Other Aids to Computation" }
@String{TablesAidsComp = "Math. Tables Aids Comput." }
@String{NumerMath = "Numerische Mathematik" }
@String{NumerMath = "Numer. Math." }
@String{PacificMath = "Pacific Journal of Mathematics" }
@String{PacificMath = "Pacific J. Math." }
@String{ParDistComp = "Journal of Parallel and Distributed Computing" }
@String{ParDistComp = "J. Parallel and Distrib. Comput." } % didn't find
@String{ParComputing = "Parallel Computing" }
@String{ParComputing = "Parallel Comput." }
@String{PhilMag = "Philosophical Magazine" }
@String{PhilMag = "Philos. Mag." }
@String{ProcNAS = "Proceedings of the National Academy of Sciences
of the USA" }
@String{ProcNAS = "Proc. Nat. Acad. Sci. U. S. A." }
@String{Psychometrika = "Psychometrika" }
@String{Psychometrika = "Psychometrika" }
@String{QuartMath = "Quarterly Journal of Mathematics, Oxford, Series (2)" }
@String{QuartMath = "Quart. J. Math. Oxford Ser. (2)" }
@String{QuartApplMath = "Quarterly of Applied Mathematics" }
@String{QuartApplMath = "Quart. Appl. Math." }
@String{RevueInstStat = "Review of the International Statisical Institute" }
@String{RevueInstStat = "Rev. Inst. Internat. Statist." }
%SIAM
@String{JSIAM = "Journal of the Society for Industrial and Applied
Mathematics" }
@String{JSIAM = "J. Soc. Indust. Appl. Math." }
@String{JSIAMB = "Journal of the Society for Industrial and Applied
Mathematics, Series B, Numerical Analysis" }
@String{JSIAMB = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal." }
@String{SIAMAlgMeth = "{SIAM} Journal on Algebraic and Discrete Methods" }
@String{SIAMAlgMeth = "{SIAM} J. Algebraic Discrete Methods" }
@String{SIAMAppMath = "{SIAM} Journal on Applied Mathematics" }
@String{SIAMAppMath = "{SIAM} J. Appl. Math." }
@String{SIAMComp = "{SIAM} Journal on Computing" }
@String{SIAMComp = "{SIAM} J. Comput." }
@String{SIAMMatrix = "{SIAM} Journal on Matrix Analysis and Applications" }
@String{SIAMMatrix = "{SIAM} J. Matrix Anal. Appl." }
@String{SIAMNumAnal = "{SIAM} Journal on Numerical Analysis" }
@String{SIAMNumAnal = "{SIAM} J. Numer. Anal." }
@String{SIAMReview = "{SIAM} Review" }
@String{SIAMReview = "{SIAM} Rev." }
@String{SIAMSciStat = "{SIAM} Journal on Scientific and Statistical
Computing" }
@String{SIAMSciStat = "{SIAM} J. Sci. Statist. Comput." }
@String{SoftPracExp = "Software Practice and Experience" }
@String{SoftPracExp = "Software Prac. Experience" } % didn't find in AMS MR
@String{StatScience = "Statistical Science" }
@String{StatScience = "Statist. Sci." }
@String{Techno = "Technometrics" }
@String{Techno = "Technometrics" }
@String{USSRCompMathPhys = "{USSR} Computational Mathematics and Mathematical
Physics" }
@String{USSRCompMathPhys = "{U. S. S. R.} Comput. Math. and Math. Phys." }
@String{VLSICompSys = "Journal of {VLSI} and Computer Systems" }
@String{VLSICompSys = "J. {VLSI} Comput. Syst." }
@String{ZAngewMathMech = "Zeitschrift fur Angewandte Mathematik und
Mechanik" }
@String{ZAngewMathMech = "Z. Angew. Math. Mech." }
@String{ZAngewMathPhys = "Zeitschrift fur Angewandte Mathematik und Physik" }
@String{ZAngewMathPhys = "Z. Angew. Math. Phys." }
@String{Academic = "Academic Press" }
@String{ACMPress = "{ACM} Press" }
@String{AdamHilger = "Adam Hilger" }
@String{AddisonWesley = "Addison-Wesley" }
@String{AllynBacon = "Allyn and Bacon" }
@String{AMS = "American Mathematical Society" }
@String{Birkhauser = "Birkha{\"u}ser" }
@String{CambridgePress = "Cambridge University Press" }
@String{Chelsea = "Chelsea" }
@String{ClaredonPress = "Claredon Press" }
@String{DoverPub = "Dover Publications" }
@String{Eyolles = "Eyolles" }
@String{HoltRinehartWinston = "Holt, Rinehart and Winston" }
@String{Interscience = "Interscience" }
@String{JohnsHopkinsPress = "The Johns Hopkins University Press" }
@String{JohnWileySons = "John Wiley and Sons" }
@String{Macmillan = "Macmillan" }
@String{MathWorks = "The Math Works Inc." }
@String{McGrawHill = "McGraw-Hill" }
@String{NatBurStd = "National Bureau of Standards" }
@String{NorthHolland = "North-Holland" }
@String{OxfordPress = "Oxford University Press" } %address Oxford or London?
@String{PergamonPress = "Pergamon Press" }
@String{PlenumPress = "Plenum Press" }
@String{PrenticeHall = "Prentice-Hall" }
@String{SIAMPub = "{SIAM} Publications" }
@String{Springer = "Springer-Verlag" }
@String{TexasPress = "University of Texas Press" }
@String{VanNostrand = "Van Nostrand" }
@String{WHFreeman = "W. H. Freeman and Co." }
@Article{Aas71,
author = "J. O. Aasen",
year = "1971",
title = "On the Reduction of a Symmetric Matrix to Tridiagonal
Form",
journal = BIT,
volume = "11",
pages = "233--242",
}
@Article{Abd71,
author = "N. N. Abdelmalek",
year = "1971",
title = "Roundoff Error Analysis for {Gram}-{Schmidt} Method
and Solution of Linear Least Squares Problems",
journal = BIT,
volume = "11",
pages = "1345--1368",
}
@Article{Ada85,
author = "L. Adams",
year = "1985",
title = "{m}-step Preconditioned Conjugate Gradient Methods",
journal = SIAMSciStat,
volume = "6",
pages = "452--463",
}
@Article{AdaC84,
author = "L. Adams and T. Crockett",
year = "1984",
title = "Modelling Algorithm Execution Time on Processor
Arrays",
journal = Computer,
volume = "17",
pages = "38--43",
}
@Article{AlePP88,
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 = LinAlgApp,
volume = "98",
pages = "3--40",
}
@Article{All73,
author = "E. L. Allgower",
year = "1973",
title = "Exact Inverses of Certain Band Matrices",
journal = NumerMath,
volume = "21",
pages = "279--284",
}
@Techreport{AmiM65,
author = "A. R. Amir-Moez",
year = "1965",
title = "Extremal Properties of Linear Transformations and
Geometry of Unitary Spaces",
institution = "Texas Tech University",
type = "Mathematics Series",
number = "243",
address = "Lubbock, TX, USA",
}
@Article{AndK75,
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",
}
@Article{AndL73,
author = "P. Anderson and G. Loizou",
year = "1973",
title = "On the Quadratic Convergence of an Algorithm that
Diagonalizes a Complex Symmetric Matrix",
journal = InstMathApp,
volume = "12",
pages = "261--271",
}
@Article{AndL76,
author = "P. Anderson and G. Loizou",
year = "1976",
title = "A {Jacobi}-Type Method for Complex Symmetric Matrices
({Handbook})",
journal = NumerMath,
volume = "25",
pages = "347--363",
}
@Article{AndOU87,
author = "T. W. Anderson and I. Olkin and L. G. Underhill",
year = "1987",
title = "Generation of Random Orthogonal Matrices",
journal = SIAMSciStat,
volume = "8",
pages = "625--629",
}
@Article{AndS83,
author = "G. Andrews and F. B. Schneider",
year = "1983",
title = "Concepts and Notations for Concurrent Programming",
journal = CompServ,
volume = "15",
pages = "1--43",
}
@Article{Arn51,
author = "W. E. Arnoldi",
year = "1951",
title = "The Principle of Minimized Iterations in the Solution
of the Matrix Eigenvalue Problem",
journal = QuartApplMath,
volume = "9",
pages = "17--29",
}
@Techreport{ArbG87,
author = "P. Arbenz and G. H. Golub",
year = "1987",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Subject to Indefinite Low Rank Perturbations with
Applications",
number = "NA 87-07",
institution = "Computer Science, Stanford University",
address = "Stanford, CA, USA",
}
@Article{ArbGG88,
author = "P. Arbenz and W. Gander and G. H. Golub",
year = "1988",
title = "Restricted Rank Modification of the Symmetric
Eigenvalue Problem: Theoretical Considerations",
journal = LinAlgApp,
volume = "104",
pages = "75--95",
}
@Article{ArbG88,
author = "P. Arbenz and G. H. Golub",
year = "1988",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Subject to Indefinite Low Rank Perturbations with
Applications",
journal = SIAMMatrix,
volume = "9",
pages = "40--58",
}
@Techreport{AriDD88,
author = "M. Arioli and J. W. Demmel and I. S. Duff",
year = "1988",
title = "Solving Sparse Linear Systems with Sparse Backward
Error",
number = "CSS 214",
institution = "Computer Science and Systems Division, AERE Harwell",
address = "Didcot, UK",
}
@Article{AriR85,
author = "M. Arioli and F. Romani",
year = "1985",
title = "Relations Between Condition Numbers and the
Convergence of the {Jacobi} Method for Real Positive
Definite Matrices",
journal = NumerMath,
volume = "46",
pages = "31--42",
}
@Article{AriL85,
author = "M. Arioli and A. Laratta",
year = "1985",
title = "Error Analysis of an Algorithm for Solving an
Underdetermined System",
journal = NumerMath,
volume = "46",
pages = "255--268",
}
@Techreport{ArmC76,
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",
}
@Article{ArnL84,
author = "W. F. Arnold and A. J. Laub",
year = "1984",
title = "Generalized Eigenproblem Algorithms and Software for
Algebraic {Riccati} Equations",
journal = ProcIEEE,
volume = "72",
pages = "1746--1754",
}
@Phdthesis{Ash87,
author = "S. F. Ashby",
year = "1987",
title = "Polynomial Preconditioning for Conjugate Gradient
Methods",
school = "Computer Science, University of Illinois",
address = "ILL",
}
@Techreport{AshMS88,
author = "S. Ashby and T. A. Manteuffel and P. E. Saylor",
year = "1988",
title = "A Taxonomy for Conjugate Gradient Methods",
number = "UCRL-98508",
institution = "Lawrence Livermore National Laboratory",
address = "Livermore, CA, USA",
}
@Article{Asp59,
author = "E. Asplund",
year = "1959",
title = "Inverse of Matrices {$\{a_{ij}\}$} Which Satisfy
{$a_{ij} = 0$, $j > i+p$}",
journal = MathScand,
volume = "7",
pages = "57--60",
}
@Incollection{Axe77,
author = "O. Axelsson",
year = "1977",
title = "Solution of Linear Systems of Equations: Iterative
Methods",
booktitle = "Sparse Matrix Techniques: {Copenhagen}, 1976",
editor = "V. A. Barker",
publisher = Springer,
address = "Berlin, Germany",
}
@Article{Axe80,
author = "O. Axelsson",
year = "1980",
title = "Conjugate Gradient Type Methods for Unsymmetric and
Inconsistent Systems of Linear Equations",
journal = LinAlgApp,
volume = "29",
pages = "1--66",
}
@Article{Axe85,
author = "O. Axelsson",
year = "1985",
title = "A Survey of Preconditioned Iterative Methods for
Linear Systems of Equations",
journal = BIT,
volume = "25",
pages = "166--187",
}
@Article{AxeP86,
author = "O. Axelsson and B. Polman",
year = "1986",
title = "On Approximate Factorization Methods for Block
Matrices Suitable for Vector and Parallel Processors",
journal = LinAlgApp,
volume = "77",
pages = "3--26",
}
@Article{Bai88a,
author = "Z. Bai",
year = "1988",
title = "Note on the Quadratic Convergence of {Kogbetliantz}'s
Algorithm for Computing the Singular Value
Decomposition",
journal = LinAlgApp,
volume = "104",
pages = "131--140",
}
@Article{Bai88b,
author = "D. Bailey",
year = "1988",
title = "Extra High Speed Matrix Multiplication on the
{Cray}-2",
journal = SIAMSciStat,
volume = "9",
pages = "603--607",
}
@Article{BarI75,
author = "I. Y. Bar-Itzhack",
year = "1975",
title = "Iterative Optimal Orthogonalization of the Strapdown
Matrix",
journal = IEEETransAeroElec,
volume = "11",
pages = "30--37",
}
@Article{Bar87,
author = "J. L. Barlow",
year = "1987",
title = "On the Smallest Positive Singular Value of an
{$M$}-Matrix with Applications to Ergodic {Markov}
Chains",
journal = SIAMAlgMeth,
volume = "7",
pages = "414--424",
}
@Article{BarNP88,
author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons",
year = "1988",
title = "Iterative Methods for Equality Constrained Least
Squares Problems",
journal = SIAMSciStat,
volume = "9",
pages = "892--906",
}
@Article{BarS68,
author = "S. Barnett and C. Storey",
year = "1968",
title = "Some Applications of the {Lyapunov} Matrix Equation",
journal = InstMathApp,
volume = "4",
pages = "33--42",
}
@Article{BarP75a,
author = "I. Barrodale and C. Phillips",
year = "1975",
title = "Algorithm~495: Solution of an Overdetermined System
of Linear Equations in the {Chebychev} Norm",
journal = ACMMathSoft,
volume = "1",
pages = "264--270",
}
@Article{BarR73,
author = "I. Barrodale and F. D. K. Roberts",
year = "1973",
title = "An Improved Algorithm for Discrete {$L_{1}$} Linear
Approximation",
journal = SIAMNumAnal,
volume = "10",
pages = "839--848",
}
@Article{Bar71,
author = "R. H. Bartels",
year = "1971",
title = "A Stabilization of the Simplex Method",
journal = NumerMath,
volume = "16",
pages = "414--434",
}
@Article{BarCC78,
author = "R. H. Bartels and A. R. Conn and C. Charalambous",
year = "1978",
title = "On {Cline}'s Direct Method for Solving Overdetermined
Linear Systems in the {$L_{\infty}$} Sense",
journal = SIAMNumAnal,
volume = "15",
pages = "255--270",
}
@Article{BarCS78,
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 = SIAMNumAnal,
volume = "15",
pages = "224--241",
}
@Article{BarS72,
author = "R. H. Bartels and G. W. Stewart",
year = "1972",
title = "Solution of the Equation {$AX + XB = C$}",
journal = CACM,
volume = "15",
pages = "820--826",
}
@Article{BarMW67,
author = "W. Barth and 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 = NumerMath,
volume = "9",
pages = "386--393",
note = "Also in \cite[pages 249--256]{WilR71}",
}
@Article{BarG76,
author = "V. Barwell and J. A. George",
year = "1976",
title = "A Comparison of Algorithms for Solving Symmetric
Indefinite Systems of Linear Equations",
journal = ACMMathSoft,
volume = "2",
pages = "242--251",
}
@Article{BatW73,
author = "K. J. Bathe and E. L. Wilson",
year = "1973",
title = "Solution Methods for Eigenvalue Problems in
Structural Mechanics",
journal = IntNumerEng,
volume = "6",
pages = "213--226",
}
@Article{BauF60a,
author = "F. L. Bauer and C. T. Fike",
year = "1960",
title = "Norms and Exclusion Theorems",
journal = NumerMath,
volume = "2",
pages = "137--144",
}
@Article{Bau63,
author = "F. L. Bauer",
year = "1963",
title = "Optimally Scaled Matrices",
journal = NumerMath,
volume = "5",
pages = "73--87",
}
@Article{Bau65,
author = "F. L. Bauer",
year = "1965",
title = "Elimination with Weighted Row Combinations for
Solving Linear Equations and Least Squares Problems",
journal = NumerMath,
volume = "7",
pages = "338--352",
note = "Also in \cite[pages 119--133]{WilR71}",
}
@Article{BauF60b,
author = "F. L. Bauer and C. T. Fike",
year = "1960",
title = "Norms and Exclusion Theorems",
journal = NumerMath,
volume = "2",
pages = "137--144",
}
@Article{BauR68,
author = "F. L. Bauer and C. Reinsch",
year = "1968",
title = "Rational {QR} Transformation with {Newton} Shift for
Symmetric Tridiagonal Matrices",
journal = NumerMath,
volume = "11",
pages = "264--272",
note = "Also in \cite[pages 257--265]{WilR71}",
}
@Incollection{BauR70,
author = "F. L. Bauer and C. Reinsch",
year = "1970",
title = "Inversion of Positive Definite Matrices by the
{Gauss}-{Jordan} Methods",
booktitle = "Handbook for Automatic Computation Vol. 2: Linear
Algebra",
editor = "J. H. Wilkinson and C. Reinsch",
publisher = Springer,
address = "New York, NY, USA",
pages = "45--49",
}
@Article{BavS79,
author = "C. Bavely and G. W. Stewart",
year = "1979",
title = "An Algorithm for Computing Reducing Subspaces by
Block Diagonalization",
journal = SIAMNumAnal,
volume = "16",
pages = "359--367",
}
@Book{Bel70,
author = "R. Bellman",
year = "1970",
title = "Introduction to Matrix Analysis",
edition = "second",
publisher = McGrawHill,
address = "New York, NY, USA",
}
@Article{Bel73,
author = "E. Beltrami",
year = "1873",
title = "Sulle Funzioni Bilineari",
journal = GiornaleMath,
volume = "11",
pages = "98--106",
}
@Article{BenS70,
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
Non-Symmetric Matrix",
journal = CompPhys,
volume = "6",
pages = "146--149",
}
@Article{BerBI71,
author = "A. Berman and A. Ben-Israel",
year = "1971",
title = "A Note on Pencils of {Hermitian} of Symmetric
Matrices",
journal = SIAMAppMath,
volume = "21",
pages = "51--54",
}
@Article{BerV68,
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 = NumerMath,
volume = "12",
pages = "215--222",
}
@Inproceedings{BerS86,
author = "M. Berry and A. Sameh",
year = "1986",
title = "Multiprocessor {Jacobi} Algorithms for Dense
Symmetric Eigenvalue and Singular Value
Decompositions",
booktitle = "Proceedings International Conference on Parallel
Processing",
pages = "433--440",
}
@Incollection{Bis87,
author = "C. H. Bischof",
year = "1987",
title = "The Two-Sided Block {Jacobi} Method on Hypercube
Architectures",
booktitle = "Hypercube Multiprocessors",
editor = "M. T. Heath",
publisher = SIAMPub,
address = "Philadelphia, PA, USA",
}
@Techreport{Bis88a,
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, Cornell University",
address = "Ithaca, NY, USA",
}
@Phdthesis{Bis88b,
author = "C. H. Bischof",
year = "1988",
title = "{QR} Factorization Algorithms for Coarse Grain
Distributed Systems",
school = "Computer Science, Cornell University",
address = "Ithaca, NY, USA",
}
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author = "C. H. Bischof and C. Van Loan",
year = "1986",
title = "Computing the {SVD} on a Ring of Array Processors",
booktitle = "Large Scale Eigenvalue Problems",
editor = "J. Cullum and R. Willoughby",
publisher = NorthHolland,
pages = "51--66",
}
@Article{BisL87,
author = "C. H. Bischof and C. Van Loan",
year = "1987",
title = "The {WY} Representation for Products of {Householder}
Matrices",
journal = SIAMSciStat,
volume = "8",
pages = "s2--s13",
}
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author = "{\AA}. Bj{\"o}rck",
year = "1967",
title = "Iterative Refinement of Linear Least Squares
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journal = BIT,
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pages = "257--278",
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author = "{\AA}. Bj{\"o}rck",
year = "1967",
title = "Solving Linear Least Squares Problems by
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journal = BIT,
volume = "7",
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author = "{\AA}. Bj{\"o}rck",
year = "1968",
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author = "{\AA}. Bj{\"o}rck",
year = "1984",
title = "A General Updating Algorithm for Constrained Linear
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journal = SIAMSciStat,
volume = "5",
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author = "{\AA}. Bj{\"o}rck",
year = "1987",
title = "Stability Analysis of the Method of Seminormal
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journal = LinAlgApp,
volume = "88/89",
pages = "31--48",
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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 = NorthHolland,
}
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author = "{\AA}. Bj{\"o}rck and C. Bowie",
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title = "An Iterative Algorithm for Computing the Best
Estimate of an Orthogonal Matrix",
journal = SIAMNumAnal,
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pages = "358--364",
}
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author = "{\AA}. Bj{\"o}rck and T. Elfving",
year = "1973",
title = "Algorithms for Confluent {Vandermonde} Systems",
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volume = "21",
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author = "{\AA}. Bj{\"o}rck and G. H. Golub",
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title = "Iterative Refinement of Linear Least Squares
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pages = "322--337",
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author = "{\AA}. Bj{\"o}rck and G. H. Golub",
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author = "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider",
year = "1981",
title = "Large-Scale Matrix Problems",
publisher = NorthHolland,
address = "New York, NY, USA",
}
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author = "{\AA}. Bj{\"o}rck and S. Hammarling",
year = "1983",
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author = "A. W. Bojanczyk and R. P. Brent and P. Van Dooren and
F. R. de Hoog",
year = "1987",
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author = "D. L. Boley and G. H. Golub",
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pages = "63--76",
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author = "J. R. Bunch",
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author = "O. Buneman",
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@Phdthesis{Bye83,
author = "R. Byers",
year = "1983",
title = "{Hamiltonian} and Symplectic Algorithms for the
Algebraic {Riccati} Equation",
school = "Center for Applied Mathematics, Cornell University",
address = "Ithaca, NY, USA",
}
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author = "A. K. Cline",
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title = "Several observations on the Use of Conjugate Gradient
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type = "report",
number = "76-22",
institution = "ICASE, NASA Langley Research Center",
address = "Hampton, VA, USA",
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address = "New York, NY, USA",
pages = "409--426",
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author = "T. Coleman and C. Van Loan",
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author = "P. Concus and G. H. Golub and D. P. O'Leary",
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title = "A Generalized Conjugate Gradient Method for the
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booktitle = "Sparse Matrix Computations",
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publisher = Academic,
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author = "M. G. Cox",
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author = "C. R. Crawford",
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author = "C. R. Crawford and Y. S. Moon",
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author = "J. Cullum and W. E. Donath",
year = "1974",
title = "A Block {Lanczos} Algorithm for Computing the {Q}
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booktitle = "Proceedings of the 1974 IEEE Conference on Decision
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pages = "505--509",
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@Techreport{CulW77,
author = "J. Cullum and R. A. Willoughby",
year = "1977",
title = "The Equivalence of the {Lanczos} and the Conjugate
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number = "RC-6903",
institution = "IBM",
address = "Yorktown Heights, NY, USA",
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author = "J. Cullum and R. A. Willoughby",
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title = "{Lanczos} and the Computation in Specified Intervals
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publisher = SIAMPub,
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author = "J. Cullum and R. A. Willoughby",
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title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue
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author = "J. Cullum and R. A. Willoughby",
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author = "M. J. Dayde and I. S. Duff",
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number = "CSS-229",
institution = "Computer Science and Systems Division, Harwell
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address = "Oxon OX11 ORA, UK",
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Hammarling",
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title = "A Set of Level 3 {Basic} {Linear} {Algebra}
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number = "ANL-MCS-TM-88",
institution = "Argonne National Laboratory",
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R. J. Hanson",
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author = "J. J. Dongarra and S. Hammarling and D. C. Sorensen",
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number = "ANL-MCS-TM 99",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
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author = "J. J. Dongarra and L. Kaufman and S. Hammarling",
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Performance Computers",
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volume = "77",
pages = "113--136",
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author = "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
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title = "Improving the Accuracy of Computed Eigenvalues and
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title = "Implementation of Some Concurrent Algorithms for
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pages = "25--34",
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author = "P. J. Eberlein",
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author = "L. Eld{\`e}n",
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title = "Numerical Analysis of Regularization and Constrained
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number = "20",
school = "Linkoping Studies in Science and Technology",
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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",
}
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author = "L. Eld{\`e}n and R. Schreiber",
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author = "G. A. Geist and M. T. Heath",
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title = "Parallel {Cholesky} Factorization on a Hypercube
Multiprocessor",
number = "ORNL 6190",
institution = "Oak Ridge Laboratory",
address = "Oak Ridge, TN, USA",
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author = "G. A. Geist and M. T. Heath",
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title = "Matrix Factorization on a Hypercube",
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author = "G. H. Golub",
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author = "G. H. Golub",
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publisher = Academic,
address = "New York, NY, USA",
pages = "365--397",
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author = "G. H. Golub",
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volume = "15",
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author = "G. H. Golub",
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publisher = Academic,
address = "New York, NY, USA",
}
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author = "G. H. Golub and M. Heath and G. Wahba",
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a Good Ridge Parameter",
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volume = "88/89",
pages = "317--328",
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author = "G. H. Golub and W. Kahan",
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title = "Calculating the Singular Values and Pseudo-Inverse of
a Matrix",
journal = JSIAMB,
volume = "2",
pages = "205--224",
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author = "G. H. Golub and V. Klema and G. W. Stewart",
year = "1976",
title = "Rank Degeneracy and Least Squares Problems",
number = "TR-456",
institution = "Computer Science, University of Maryland",
address = "College Park, MD, USA",
}
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author = "G. H. Golub and F. T. Luk and M. Overton",
year = "1981",
title = "A Block {Lanczos} Method for Computing the Singular
Values and Corresponding Singular Vectors of a Matrix",
journal = ACMMathSoft,
volume = "7",
pages = "149--169",
}
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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, France",
}
@Article{GolM86,
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 {Markov} Chains",
journal = SIAMAlgMeth,
volume = "7",
pages = "273--281",
}
@Article{GolNL79,
author = "G. H. Golub and S. Nash and C. Van Loan",
year = "1979",
title = "A {Hessenberg}-{Schur} Method for the Matrix Problem
{$AX + XB = C$}",
journal = IEEETransAC,
volume = "AC-24",
pages = "909--913",
}
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author = "G. H. Golub and M. Overton",
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institution = "Mathematics, University of Manchester",
address = "UK",
note = "To appear in Proceedings of the IMA Conference on
Applications of Matrix Theory, eds. S. Barnett and
M. J. C. Gover",
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institution = "Computer Science, Yale University",
address = "New Haven, CT, USA",
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title = "Algorithms for Multiplying Matrices of Arbitrary
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number = "YALEU DCS RR-569",
institution = "Computer Science, Yale University",
address = "New Haven, CT, USA",
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author = "B. K{\aa}gstr{\"o}m and P. Ling",
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number = "UMINF-154.88",
institution = "Information Processing, University of Ume{\aa}",
address = "S-901 87 Ume{\aa}, Sweden",
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year = "1988",
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author = "G. W. Stewart",
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address = "New York, NY, USA",
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author = "G. W. Stewart",
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author = "G. W. Stewart",
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address = "New York, NY, USA",
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author = "G. W. Stewart",
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volume = "25",
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author = "G. W. Stewart",
year = "1976",
title = "Simultaneous Iteration for Computing Invariant
Subspaces of Non-{Hermitian} Matrices",
journal = NumerMath,
volume = "25",
pages = "12--36",
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author = "G. W. Stewart",
year = "1977",
title = "On the Perturbation of Pseudo-Inverses, Projections,
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volume = "19",
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author = "G. W. Stewart",
year = "1977",
title = "Perturbation Bounds for the {QR} Factorization of a
Matrix",
journal = SIAMNumAnal,
volume = "14",
pages = "509--518",
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@Techreport{Ste77c,
author = "G. W. Stewart",
year = "1977",
title = "Sensitivity Coefficients for the Effects of Errors in
the Independent Variables in a Linear Regression",
number = "TR-571",
institution = "Computer Science, University of Maryland",
address = "College Park, MD, USA",
}
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author = "G. W. Stewart",
year = "1978",
title = "Perturbation Theory for the Generalized Eigenvalue
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booktitle = "Recent Advances in Numerical Analysis",
editor = "C. de Boor and G. H. Golub",
publisher = Academic,
address = "New York, NY, USA",
}
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author = "G. W. Stewart",
year = "1979",
title = "A Note on the Perturbation of Singular Values",
journal = LinAlgApp,
volume = "28",
pages = "213--216",
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author = "G. W. Stewart",
year = "1979",
title = "Perturbation Bounds for the Definite Generalized
Eigenvalue Problem",
journal = LinAlgApp,
volume = "23",
pages = "69--86",
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author = "G. W. Stewart",
year = "1979",
title = "The Effects of Rounding Error on an Algorithm for
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volume = "23",
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author = "G. W. Stewart",
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journal = SIAMNumAnal,
volume = "17",
pages = "403--409",
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author = "G. W. Stewart",
year = "1981",
title = "On the Implicit Deflation of Nearly Singular Systems
of Linear Equations",
journal = SIAMSciStat,
volume = "2",
pages = "136--140",
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author = "G. W. Stewart",
year = "1983",
title = "A Method for Computing the Generalized Singular Value
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booktitle = "Matrix Pencils",
editor = "B. K{\aa}gstr{\"o}m and A. Ruhe",
publisher = Springer,
address = "New York, NY, USA",
pages = "207--220",
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author = "G. W. Stewart",
year = "1984",
title = "Rank Degeneracy",
journal = SIAMSciStat,
volume = "5",
pages = "403--413",
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author = "G. W. Stewart",
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title = "On the Asymptotic Behavior of Scaled Singular Value
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journal = MathComp,
volume = "43",
pages = "483--490",
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author = "G. W. Stewart",
year = "1984",
title = "A Second Order Perturbation Expansion for Small
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journal = LinAlgApp,
volume = "56",
pages = "231--236",
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author = "G. W. Stewart",
year = "1984",
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journal = NumerMath,
volume = "33,34",
pages = "61--66",
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author = "G. W. Stewart",
year = "1985",
title = "A {Jacobi}-Like Algorithm for Computing the {Schur}
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institution = "Department of Electrical Engineering, Katholieke
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