@Preamble{
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"
}
@String{j-ANN-OPER-RESEARCH = "Annals of Operations Research"}
@String{j-APPL-MATH-MODEL = "Applied Mathematical Modelling"}
@String{j-COMPUTING = "Computing"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-EUROMATH-BULL = "Euromath Bulletin"}
@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical Engineering"}
@String{j-INTERVAL-COMP = "Interval Computations"}
@String{j-J-COMPLEXITY = "Journal of complexity"}
@String{j-J-GLOBAL-OPT = "Journal of Global Optimization"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-OPTIM-METHODS-SOFTW = "Optimization Methods \& Software"}
@String{j-RELIABLE-COMPUTING = "Reliable Computing = Nadezhnye vychisleniia"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-OPT = "SIAM Journal on Optimization"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical
Computing"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@String{pub-AKADEMIE-VERLAG = "Akademie-Verlag"}
@String{pub-AKADEMIE-VERLAG:adr = "Berlin"}
@String{pub-AMS = "Amer. Math. Soc."}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-BALTZER = "J. C. Baltzer AG, Scientific
Publishing Company"}
@String{pub-BALTZER:adr = "Basel, Switzerland"}
@String{pub-BIRKHAUSER = "Birkh{\"a}user"}
@String{pub-BIRKHAUSER:adr = "Cambridge, MA, USA; Berlin, Germany; Basel,
Switzerland"}
@String{pub-CRC = "CRC Press"}
@String{pub-CRC:adr = "2000 N.W. Corporate Blvd., Boca Raton, FL
33431-9868, USA"}
@String{pub-IEEE = "IEEE Computer Society Press"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300,
Silver Spring, MD 20910, USA"}
@String{pub-IMACS = "IMACS"}
@String{pub-IMACS:adr = "Department of Computer Science,
Rutgers University, New Brunswick,
NJ"}
@String{pub-KLUWER = "Kluwer Academic Publishers"}
@String{pub-KLUWER:adr = "Dordrecht, The Netherlands"}
@String{pub-NORTH-HOLLAND = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr = "Amsterdam, The Netherlands"}
@String{pub-SIAM = "SIAM"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SPRINGER-WIEN = "Spring{\-}er"}
@String{pub-SPRINGER-WIEN:adr = "Wien / New York"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-SV-CHAM = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV-CHAM:adr = "Cham, Switzerland"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@MastersThesis{Kearfott:1972:MC,
author = "Ralph Baker Kearfott",
title = "The method of characteristics",
type = "{Bachelor of Science Honors degree}",
school = "Department of Mathematics, University of Utah",
address = "Salt Lake City, UT, USA 84112",
pages = "iv + 74",
year = "1972",
bibdate = "Tue Aug 24 10:00:44 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Kearfott:1977:CDM,
author = "Ralph Baker Kearfott",
title = "Computing the degree of maps and a generalized method
of bisection",
type = "{Ph.D.} thesis",
school = "Department of Mathematics, University of Utah",
address = "Salt Lake City, UT, USA 84112",
pages = "x + 159 + 1",
year = "1977",
bibdate = "Tue Aug 24 10:02:12 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
advisor = "Frank Stenger",
}
@Article{Kearfott:1978:PCE,
author = "Baker Kearfott",
title = "A Proof of Convergence and an Error Bound for the
Method of Bisection in {$ {\bf R}^n $}",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1147--1153",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65H10 (Systems of nonlinear equations (numerical
methods)); 05-04 (Machine computation, programs
(combinatorics)); 55M25 (Degree, winding number)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
JSTOR database",
ZMnumber = "0395.65021",
acknowledgement = ack-nhfb,
classcodes = "C4110 (Error analysis in numerical methods)",
corpsource = "Dept. of Math. and Statistics, Univ. of Southwestern
Louisiana, Lafayette, LA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "bisection in $R^n$; convergence of numerical methods;
error analysis; error bound; method of; proof of
convergence; simplex",
treatment = "T Theoretical or Mathematical",
}
@Article{Kearfott:1979:EDC,
author = "Baker Kearfott",
title = "An efficient degree-computation method for a
generalized method of bisection",
journal = j-NUM-MATH,
volume = "32",
number = "2",
pages = "109--127",
month = jun,
year = "1979",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01404868",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65J05 (65H05); 65H10 (Systems of nonlinear equations
(numerical methods)); 55M25 (Degree, winding number)",
MRnumber = "80g:65062",
MRreviewer = "Romesh Saigal",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0386.65016",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "Dept. of Math., Univ. of Southwestern Louisiana,
Lafayette, LA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "bisection generalised method; efficient
degree-computation; matrix algebra; method of
bisection; numerical methods",
treatment = "A Application; T Theoretical or Mathematical",
}
@InCollection{Kearfott:1979:SRE,
author = "R. Baker Kearfott",
editor = "V. Lakshmikantham",
booktitle = "{Applied nonlinear analysis: proceedings of an
International Conference on Applied Nonlinear Analysis,
held at the University of Texas at Arlington,
Arlington, Texas, April 20--22, 1978}",
title = "A summary of recent experiments to compute the
topological degree",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "xx + 726",
pages = "627--633",
year = "1979",
ISBN = "0-12-434180-2",
ISBN-13 = "978-0-12-434180-7",
LCCN = "QA300 .I48 1978",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0454.65040",
classmath = "{65H10 (Systems of nonlinear equations (numerical
methods)) 55M25 (Degree, winding number) 58C99
(Calculus on manifolds) }",
keywords = "Brouwer degree; test problems; topological (or
combinatorial) algorithms; topological degree",
}
@Article{Kearfott:1980:MIN,
author = "R. B. Kearfott and R. D. Sidman and D. Smith",
booktitle = "IEEE 1980 Frontiers of Engineering in Health Care
(137--140)",
title = "A method for identifying noise-free evoked potentials
application of {DLM} (Dipole Localization Method) to
these components",
journal = j-IEEE-TRANS-BIOMED-ENG,
volume = "BME-27",
number = "9",
pages = "534--534",
year = "1980",
CODEN = "IEBEAX",
ISSN = "0018-9294 (print), 1558-2531 (electronic)",
ISSN-L = "0018-9294",
bibdate = "Wed Mar 14 18:29:22 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Biomedical Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10",
}
@InCollection{Kearfott:1981:DFA,
author = "Ralph Baker Kearfott",
booktitle = "{Numerical solution of nonlinear equations,
Proceedings of the Symposium, Bremen 1980}",
title = "A derivative-free arc continuation method and a
bifurcation technique",
publisher = pub-SV,
address = pub-SV:adr,
year = "1981",
MRclass = "65H10 (Systems of nonlinear equations (numerical
methods)); 65H17 (Eigenvalue and bifurcation problems
of nonlinear algebraic equations (numerical methods))",
bibdate = "Tue Aug 24 09:48:06 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Lecture Notes in Mathematics",
ZMnumber = "0461.65038",
acknowledgement = ack-nhfb,
keywords = "arc continuation; arc continuation method; bifurcation
problems; Brouwer degree; derivative-free
predictor-corrector method; least change secant
updates; Powell's method; quasi-Newton methods",
}
@InProceedings{Smith:1982:UES,
author = "D. B. Smith and R. D. Sidman and J. S. Henke and R. B.
Kearfott",
title = "The Use of Equivalent Source Models in {EP} Research
and Differential Diagnosis",
crossref = "Cohen:1982:IFE",
pages = "64--70",
year = "1982",
bibdate = "Wed May 24 14:34:58 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Kearfott:1983:CMP,
author = "Ralph Baker Kearfott",
title = "Continuation Methods and Parametrized Nonlinear Least
Squares: Techniques and Experiments",
crossref = "Pereyra:1982:NM",
pages = "142--150",
year = "1983",
MRclass = "65K05 (Mathematical programming (numerical methods));
65H10 (Systems of nonlinear equations (numerical
methods)); 65C99 (Probabilistic methods, simulation and
stochastic differential equations (numerical analysis))
90C30 (Nonlinear programming); 62J05 (Linear
regression)",
bibdate = "Fri May 9 19:07:42 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
series = "Lecture Notes in Mathematics",
ZMnumber = "0519.65040",
acknowledgement = ack-nhfb,
keywords = "continuation methods; nonlinear least squares;
quasi-Newton updates; statistical parameter fitting",
xxpages = "142--151",
xxpages = "140--150",
}
@Article{Kearfott:1983:SAI,
author = "Ralph Baker Kearfott",
title = "A Sinc Approximation for the Indefinite Integral",
journal = j-MATH-COMPUT,
volume = "41",
number = "164",
pages = "559--572",
month = oct,
year = "1983",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007693",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D30 (41A99)",
MRnumber = "85g:65029",
MRreviewer = "B. Boyanov",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
JSTOR database",
ZMnumber = "0523.65018",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kearfott:1983:SGB,
author = "Ralph Baker Kearfott",
title = "Some general bifurcation techniques",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "4",
number = "1",
pages = "52--68",
month = mar,
year = "1983",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0904004",
ISSN = "0196-5204",
MRclass = "65H10 (58C40 58E07)",
MRnumber = "84f:65047",
MRreviewer = "Eugene Allgower",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0511.65034",
acknowledgement = ack-nhfb,
classification = "C4150 (Nonlinear and functional equations)",
corpsource = "Dept. of Math., Southwestern Louisiana Univ.,
Lafayette, LA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "derivative-free arc-following method; determinant;
finite differences; Jacobi matrix; multiple bifurcation
points; nonlinear equations; primary bifurcation
points; secondary bifurcation points",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kearfott:1984:GTF,
author = "Ralpha Baker Kearfott",
title = "On a General Technique for Finding Directions
Proceeding from Bifurcation Points",
crossref = "Kuepper:1984:NMB",
pages = "210--218",
year = "1984",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "539.65038",
abstract = "Various quite satisfactory analytical and numerical
techniques are available for analysing bifurcation
points when something about the structure is known a
priori. The author previously introduced a method
applicable when such information is not present, or
when the arcs intersect tangentially. That method is
discussed here, with particular emphasis on avenues to
improvement in efficiency and reliability.",
}
@Article{Kearfott:1987:AGB,
author = "R. Baker Kearfott",
title = "Abstract Generalized Bisection and a Cost Bound",
journal = j-MATH-COMPUT,
volume = "49",
number = "179",
pages = "187--202",
month = jul,
year = "1987",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008257",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65H10 (Systems of nonlinear equations (numerical
methods)); 65K05 (Mathematical programming (numerical
methods)); 90C30 (Nonlinear programming); 68Q25
(Analysis of algorithms and problem complexity)",
MRnumber = "88h:65109",
MRreviewer = "T. L. Freeman",
bibdate = "Tue Aug 24 09:36:53 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
JSTOR database",
ZMnumber = "0632.65055",
abstract = "The purpose of this paper is to study desirable
properties of binary search algorithms for isolating
all solutions to nonlinear systems of equations $ F(X)
= 0 $ within a given compact domain $ D \in \Bbb R \sp
n $. We devise a general framework such that any
algorithm fitting into the general framework will
always isolate all solutions $ Z \in D $ such that $
F(Z) = 0 $; this framework contains a new idea for
handling the occurrence of roots on boundaries. We then
present and prove a bound on the total amount of
computation which is valid for any algorithm in the
class. \par
Finally, we define a specific prototypical algorithm
valid for $F$ satisfying certain natural smoothness
properties; we show that it satisfies the hypotheses
for the general framework. This algorithm is based on
``bisection'' of generalized rectangles, the
Kantorovich theorem, and second-order Taylor type
models for $F$. It is meant to provide further
guidelines for the development of effective heuristics,
etc., for actual implementations.",
acknowledgement = ack-nhfb,
classcodes = "C4200 (Computer theory)",
corpsource = "Dept. of Math., Southwestern Louisiana Univ.,
Lafayette, LA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "abstract generalized bisection; analysis of
algorithms; binary search algorithms; bound;
boundaries; compact domain; computation; computation
theory; cost bound; desirable properties; framework;
generalized bisection; generalized rectangles; global
optimization; heuristics; Kantorovich theorem; natural
smoothness; nonlinear equations systems; properties;
prototypical algorithm; roots; second-order Taylor type
models",
reviewer = "E. Allgower",
treatment = "T Theoretical or Mathematical",
}
@Misc{Kearfott:1987:INM,
author = "R. B. Kearfott",
title = "An Interval {Newton} Method for Nonlinear Least
Squares",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Kearfott:1987:SFF,
author = "R. B. Kearfott and K. Sikorski and F. Stenger",
title = "A Sinc Function Fast {Poisson} Solver",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1987:STG,
author = "R. Baker Kearfott",
title = "Some Tests of Generalized Bisection",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "197--220",
month = sep,
year = "1987",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65H10",
MRnumber = "88m:65081",
bibdate = "Sat Nov 19 13:08:33 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "See also \cite{Kearfott:1988:CTG}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p197-kearfott/",
ZMnumber = "0632.65056",
abstract = "This paper addresses the task of reliably finding
approximations to all solutions to a system of
nonlinear equations within a region defined by bounds
on each of the individual coordinates. Various forms of
generalized bisection were proposed some time ago for
this task. This paper systematically compares such
generalized bisection algorithms to themselves, to
continuation methods, and to hybrid steepest
descent/quasi-Newton methods. A specific algorithm
containing novel ``expansion'' and ``exclusion'' steps
is fully described, and the effectiveness of these
steps is evaluated. A test problem consisting of a
small, high-degree polynomial system that is
appropriate for generalized bisection, but very
difficult for continuation methods, is presented. This
problem forms part of a set of 17 test problems from
published literature on the methods being compared;
this test set is fully described here.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "``expansion'' and ``exclusion'' steps; algorithms;
continuation methods; generalized bisection; global
constrained optimization; homotopy; homotopy method;
hybrid steepest descent\slash quasi-Newton methods;
interval arithmetic; performance; quasi-Newton method;
test problem; theory",
reviewer = "E. Allgower",
subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Systems of
equations. {\bf G.1.5}: Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
Polynomials, methods for.",
}
@InProceedings{Ford:1988:RPA,
author = "M. R. Ford and R. D. Sidman and R. B. Kearfott",
title = "Resting and {P300} Auditory Responses in Normal
Subjects and Psychiatric Patients: Analysis using {DLM}
and Brain Imager",
crossref = "Vichnevetsky:1988:PTI3",
pages = "739--740",
year = "1988",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Hill:1988:IPE,
author = "C. D. Hill and R. B. Kearfott and R. D. Sidman",
title = "The Inverse Problem of Electroencephalography Using an
Imaging Technique for Simulating Cortical Surface
Data",
crossref = "Vichnevetsky:1988:PTI3",
pages = "729--734",
year = "1988",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1988:CTG,
author = "R. Baker Kearfott",
title = "Corrigenda: ``{Some} Tests of Generalized
Bisection''",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "399--399",
month = dec,
year = "1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "399 (1989). 65H10",
MRnumber = "1 062 485, 88m:65081",
bibdate = "Sat Nov 19 13:04:08 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "See \cite{Kearfott:1987:STG}.",
ZMnumber = "0666.65040",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "continuation methods; expansion and exclusion steps;
generalized bisection; global constrained optimization;
homotopy; homotopy method; hybrid steepest
descent/quasi-Newton methods; interval arithmetic;
quasi-Newton method; test problem",
}
@InProceedings{Kearfott:1988:HSS,
author = "R. B. Kearfott",
title = "On Handling Singular Systems with Interval {Newton}
Methods",
crossref = "Vichnevetsky:1988:PTI4",
pages = "651--653",
year = "1988",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Kearfott:1988:RHT,
author = "R. B. Kearfott",
title = "The Role of Homotopy Techniques in Biomedical
Modelling: {A} Case Study",
crossref = "Vichnevetsky:1988:PTI3",
pages = "732--734",
year = "1988",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Sidman:1988:IPE,
author = "R. D. Sidman and R. B. Kearfott and C. Schlichting",
title = "The Inverse Problem of Electroencephalography Assuming
Double Layer Neural Generators",
crossref = "Vichnevetsky:1988:PTI3",
pages = "726--728",
year = "1988",
bibdate = "Tue May 23 16:48:34 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Hu:1989:WCR,
author = "C.-Y. Hu and R. B. Kearfott",
title = "A Width Characterization and Row Selection Strategy
for the Interval {Gauss--Seidel} Method",
year = "1989",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1989:HSS,
author = "R. B. Kearfott",
title = "On Handling Singular Systems with Interval {Newton}
Methods",
journal = "IMACS Annals on Computing and Applied Mathematics:
Numerical and Applied Mathematics",
volume = "1.2",
pages = "653--655",
year = "1989",
ISSN = "1012-2435",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Kearfott:1989:IAM,
author = "R. B. Kearfott",
title = "Interval Arithmetic Methods for Nonlinear Systems and
Nonlinear Optimization: Introduction and Status",
crossref = "Sharda:1989:IRC",
pages = "533--542",
year = "1989",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Kearfott:1989:IMT,
author = "R. Baker Kearfott",
title = "Interval Mathematics Techniques for Control Theory
Computations",
crossref = "Bowers:1989:CC",
pages = "169--178",
year = "1989",
MRclass = "65K10 (Optimization techniques (numerical methods));
65G30 (Interval and finite arithmetic); 93C15 (Control
systems governed by ODE)",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0687.65073",
abstract = "The results are based on the fact that interval
methods can be used to find, with the rigor of a
mathematical proof, even on a computer, all roots of a
nonlinear system of equations within given bounds on
the variables. Generalized bisection together with
interval Newton methods is considered. The related
linear systems may be solved with an interval version
of the Gauss--Seidel method. The problem of finding a
global minimum for a nonlinear objective function is
considered via the system which sets the gradient equal
to zero.\par
The transfer function corresponding to a single linear
controlled ordinary differential equation is a
relational function. The above method is applied to
study the stability of such systems which depends on
the existence of roots in the right half of the complex
plane. The problem of how practical such methods are is
discussed. It is also suggested that interval methods
might be applicable to discretizations of optimal
control problems governed by ordinary differential
equations.",
}
@Misc{Kearfott:1989:ISC,
author = "R. B. Kearfott",
title = "An Interval Step Control for Continuation Methods",
year = "1989",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Sidman:1989:DAM,
author = "R. D. Sidman and R. B. Kearfott and D. J. Major and C.
D. Hill and M. R. Ford and D. B. Smith and L. Lee and
R. Kramer",
title = "Development and Application of Mathematical Techniques
for the Non-Invasive Localization of Sources of
Scalp-Recorded Electic Potentials",
crossref = "Potvin:1982:FEH",
pages = "133--157",
year = "1989",
bibdate = "Tue May 23 16:49:36 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@PhdThesis{Hu:1990:PINa,
author = "C.-Y. Hu",
title = "Preconditioners for Interval {Newton} Methods",
school = "University of Southwestern Louisiana",
year = "1990",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Hu:1990:PINb,
author = "C. Hu and R. B. Kearfott and Q. Yang",
title = "The Preconditioned Interval {Newton} Method on an
{MIMD} Computer",
year = "1990",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Hu:1990:PSI,
author = "Chen-Yi Hu and R. Baker Kearfott",
title = "A Pivoting Scheme for the Interval {Gauss--Seidel}
Method: Numerical Experiments",
crossref = "Law:1990:AOC",
pages = "97--100",
year = "1990",
MRclass = "65H10 (Systems of nonlinear equations (numerical
methods))",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0939.65523",
}
@Article{Kearfott:1990:AIP,
author = "R. Baker Kearfott and Manuel {Novoa III}",
title = "Algorithm 681: {INTBIS}, a Portable Interval
{Newton}\slash Bisection Package",
journal = j-TOMS,
volume = "16",
number = "2",
pages = "152--157",
month = jun,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:09:48 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p152-kearfott/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms; theory",
subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Systems of
equations. {\bf G.1.2}: Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
}
@InProceedings{Kearfott:1990:IAT,
author = "R. Baker Kearfott",
title = "Interval Arithmetic Techniques in the Computational
Solution of Nonlin ear Systems of Equations:
Introduction, Examples, and Comparisons",
crossref = "Allgower:1990:CSN",
pages = "337--358",
year = "1990",
MRclass = "65H10 (Systems of nonlinear equations (numerical
methods)); 65K05 (Mathematical programming (numerical
methods)); 65G30 (Interval and finite arithmetic);
90C30 (Nonlinear programming)",
bibdate = "Sat May 20 16:30:49 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0695.65029",
abstract = "The author gives a short survey of the applicability
and the importance of interval arithmetic in several
fields of numerical analysis. Starting with elementary
facts in interval analysis he reviews some classes of
interval methods for solving nonlinear systems of
equations and for finding the global minimum of an
objective function in nonlinear optimization. He
compares such methods with alternate popular ones such
as hybrid techniques and continuation methods. A
stepsize control for predictor\slash corrector
continuation procedures is derived employing an
interval Newton algorithm. More than 70 references
conclude the paper.",
acknowledgement = ack-nhfb,
keywords = "bibliography; comparisons; continuation methods;
examples; global minimum; hybrid techniques; interval
analysis; interval arithmetic; interval Newton
algorithm; nonlinear optimization; nonlinear systems;
predictor\slash corrector continuation procedures;
stepsize control",
reviewer = "G. Mayer",
}
@Article{Kearfott:1990:ING,
author = "R. B. Kearfott",
title = "Interval {Newton}\slash Generalized Bisection When
There Are Singularities near Roots",
journal = j-ANN-OPER-RESEARCH,
volume = "25",
pages = "181--196",
year = "1990",
CODEN = "AOREEV",
ISSN = "0254-5330 (print), 1572-9338 (electronic)",
ISSN-L = "0254-5330",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Annals of Operations Research",
}
@Article{Kearfott:1990:PIG,
author = "R. Baker Kearfott",
title = "Preconditioners for the Interval {Gauss--Seidel}
Method",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "3",
pages = "804--822",
month = jun,
year = "1990",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0727047",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65H10 (65G10)",
MRnumber = "91d:65072",
MRreviewer = "G. Alefeld",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0713.65037",
abstract = "Let $ F : D \subseteq {\bbfR } \sp n \to {\bbfR } \sp
n $ be a differentiable function, let $B$ denote a
prescribed box in $ {\bbfR } \sp n$. The author
thoroughly investigates the problem: Find
approximations and small error bounds to all solutions
of the equation $ F(x) = 0$ in the box $B$. A
successful approach for treating this problem is
generalized bisection in conjunction with interval
Newton iteration. Algorithmic descriptions of this
method are presented. Hereby the following subproblem
has to be considered: $ A \cdot Y = R$ with $ A \in I
A$ and $ R \in I R$, where the (unknown) matrix A is
contained in a known interval IA of matrices and the
(unknown) vector $R$ is contained in a known interval $
I R$ of vectors. Bounds on the vector $Y$ are sought as
$A$ ranges over $ I A$ and $R$ ranges over $ I R$.
\par
One standard technique for solving this subproblem is
preconditioning and one sweep of interval Gauss--Seidel
elimination. The common preconditioner is the inverse
of the midpoint-matrix of IA. The author introduces a
new preconditioner that emerges from an optimality
condition and that can be obtained by solving a
specific linear programming problem. Numerical tests of
the new preconditioner in the overall algorithm
indicate that it is effective at reducing the number of
function and derivative evaluations, and often also
results in less CPU time.",
acknowledgement = ack-nhfb,
classmath = "{65H10 (Systems of nonlinear equations (numerical
methods)) 65G30 (Interval and finite arithmetic) }",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "bisection; error bounds; Gauss--Seidel-method;
interval arithmetic; interval Gauss--Seidel
elimination; interval Newton iteration;
interval-iteration; numerical tests; preconditioning",
reviewer = "H. Fischer",
}
@Article{Kearfott:1991:DAE,
author = "R. Baker Kearfott",
title = "Decomposition of Arithmetic Expressions to Improve the
Behavior of Interval Iteration for Nonlinear Systems",
journal = j-COMPUTING,
volume = "47",
number = "2",
pages = "169--191",
month = "????",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H10 (65G10 65M15)",
MRnumber = "92j:65079",
MRreviewer = "E. Kaucher",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
MathSciNet database; OCLC Contents1st database",
ZMnumber = "0739.65049",
abstract = "{In order to verify and to enclose solutions of
nonlinear systems within given boxes, the author
combines two algorithms based on interval arithmetic.
The first expands the given nonlinear system $ F(x) = 0
$ to a larger one using the code list of $F$. Solving
these new equations with respect to their variables
repeatedly according to a particular scheme
(introducing intervals and using a stack and
intersections) yields a starting interval vector for
the second algorithm which is a preconditioned interval
Gauss--Seidel method presented in an earlier paper of
the author.\par
Theoretical results complete and support the
computational method, experimental results illustrate
its efficiency. A comparison with the well-known
Hansen-Greenberg algorithm and some items for future
work conclude the paper.}",
acknowledgement = ack-nhfb,
affiliation = "Univ of Southwestern Louisiana",
affiliationaddress = "Lafayette, USA",
classification = "723; 921",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "algorithms; automatic differentiation; comparison;
computer programming --- algorithms; experimental
results; Hansen--Greenberg algorithm; interval
arithmetic; interval integration; Jacobi matrices;
mathematical techniques; mathematical techniques ---
iterative methods; nonlinear algebraic systems;
preconditioned interval Gauss--Seidel method",
reviewer = "G. Mayer (Karlsruhe)",
}
@Article{Kearfott:1991:NTM,
author = "R. B. Kearfott and R. D. Sidman and D. J. Major and C.
D. Hill",
title = "Numerical Tests of a Method for Simulating Electrical
Potentials on the Cortical Surface",
journal = j-IEEE-TRANS-BIOMED-ENG,
volume = "38",
number = "3",
pages = "294--299",
month = mar,
year = "1991",
CODEN = "IEBEAX",
DOI = "https://doi.org/10.1109/10.133212",
ISSN = "0018-9294 (print), 1558-2531 (electronic)",
ISSN-L = "0018-9294",
bibdate = "Wed Mar 14 18:31:02 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Biomedical Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10",
}
@Article{Kearfott:1991:RPI,
author = "R. Baker Kearfott and Chen-Yi Hu and Manuel {Novoa
III}",
title = "A Review of Preconditioners for the Interval
{Gauss--Seidel} Method",
journal = j-INTERVAL-COMP,
volume = "1",
number = "1",
pages = "59--85",
year = "1991",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65F35 (Matrix norms, conditioning, scaling (numerical
linear algebra)); 65H10 (Systems of nonlinear equations
(numerical methods)); 65G30 (Interval and finite
arithmetic)",
MRnumber = "1175553 (93d:65051)",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1991/interval-computations-1991-1-pp-59-85.pdf",
ZMnumber = "0835.65065",
abstract = "In interval Newton methods for finding roots of a
system of nonlinear equations with a specified box $
{\bold X} \subset {\bbf R}^n $ we transform the system
$ F(X) = 0 $ into a linear interval system $ 0 = F(M) +
{\bold F}'({\bold X})(\widetilde {{\bold X}} - M) $; we
then use the interval Gauss--Seidel method to find
bounds $ \widetilde {{\bold X}} $ to this system. To
increase the efficiency of this, we first apply
preconditioners to the linear system. Here, we review
our recent results concerning computation of
preconditioners.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "interval Gauss--Seidel method; interval Newton
methods; linear interval system; preconditioners;
system of nonlinear equations",
}
@Article{Yakovlev:1991:BSW,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} Works on Interval
Computations, {Part I}",
journal = j-INTERVAL-COMP,
volume = "1",
number = "2",
pages = "115--122",
year = "1991",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis))",
bibdate = "Mon Jan 07 08:06:38 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1991/interval-computations-1991-2-pp-115-122.pdf",
ZMnumber = "0829.65047",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@Article{Du:1992:CPG,
author = "Kaisheng Du and R. B. Kearfott",
title = "The Cluster Problem in Global Optimization: The
Univariate Case",
journal = j-COMPUTING-SUPPLEMENTUM,
volume = "9",
pages = "117--127",
year = "1992",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Computing. Supplementum",
}
@Misc{Ganesan:1992:DMU,
author = "K. Ganesan and T. Hanson and Y. Y. Yap and R. B. and
Kearfott",
title = "Demand Management for a Utility with only Fossil Fuel
Fired Thermal Generation",
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Hu:1992:PAA,
author = "C.-Y. Hu and M. Bayoumi and R. B. Kearfott and Q.
Yang",
title = "A Parallelized Algorithm for the All-Row
Preconditioned Interval {Newton}\slash Generalized
Bisection Method",
crossref = "Dongarra:1992:PFS",
pages = "205--209",
year = "1992",
bibdate = "Wed May 24 14:49:59 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@PhdThesis{Jan:1992:EPR,
author = "C.-H. Jan",
title = "Expression Parsing and Rigorous Computation of Bounds
on All Solutions to Practical Nonlinear Systems",
school = "University of Southwestern Louisiana",
month = may,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1992:IBB,
author = "R. B. Kearfott",
editor = "Panos Pardalos and others",
title = "An Interval Branch and Bound Algorithm for Bound
Constrained Optimization Problems",
journal = j-J-GLOBAL-OPT,
volume = "2",
pages = "259--280",
year = "1992",
CODEN = "JGOPEO",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Journal of Global Optimization",
journal-URL = "http://link.springer.com/journal/10898",
}
@Article{Kearfott:1992:IPF,
author = "R. Baker Kearfott and Milind Dawande and Kaishen Du
and Chenyi Hu",
title = "{INTLIB}: a portable {Fortran-77} elementary function
library",
journal = j-INTERVAL-COMP,
volume = "2",
number = "3(5)",
pages = "96--105",
year = "1992",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65Y15 (Packaged methods in numerical analysis); 65G30
(Interval and finite arithmetic); 65G10",
MRnumber = "1 253 132",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "Interval '92 (Moscow, 1992).",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1992/interval-computations-1992-3-pp-96-105.pdf",
ZMnumber = "0829.65147",
abstract = "INTLIB is meant to be a readily available, portable,
exhaustively documented interval arithmetic library,
written in standard Fortran-77. Its underlying
philosophy is to provide a standard for interval
operations to aid in efficiency transporting programs
involving interval arithmetic. The model is the BLAS
package, for basic linear algebra operations. In this
paper, we (1) outline previous packages and present
efforts, (2) explain the overall structure of the
package, as well as give descriptions of some of the
routines, and (3) mention future enhancements.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "basic linear algebra operations; BLAS package;
Fortran-77; interval arithmetic library; INTLIB",
}
@Misc{Xing:1992:EIS,
author = "Z. Xing and R. B. Kearfott",
title = "An Efficient Interval step Control for Two Dimensional
Continuation Methods",
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Yakovlev:1992:BSWa,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {II}",
journal = j-INTERVAL-COMP,
volume = "1992",
number = "1(3)",
pages = "104--111",
year = "1992",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:14:10 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0829.65048",
acknowledgement = ack-nhfb,
classmath = "{65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis)) }",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@Article{Yakovlev:1992:BSWb,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {II}",
journal = j-INTERVAL-COMP,
volume = "1",
number = "3",
pages = "104--111",
year = "1992",
CODEN = "????",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:14:10 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1992/interval-computations-1992-1-pp-104-111.pdf",
ZMnumber = "0829.65048",
acknowledgement = ack-nhfb,
classmath = "{65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis)) }",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@Article{Yakovlev:1992:BSWc,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {III}",
journal = j-INTERVAL-COMP,
volume = "2",
number = "4",
pages = "107--115",
year = "1992",
CODEN = "????",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:14:10 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1992/interval-computations-1992-2-pp-107-115.pdf",
ZMnumber = "0829.65049",
acknowledgement = ack-nhfb,
classmath = "65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis))",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@MastersThesis{Dawande:1993:ASA,
author = "M. W. Dawande",
title = "Augmented System Approach for Solving the Least
Squares Problem in an Interior Point Method for Linear
Programming",
school = "University of Southwestern Louisiana",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Hu:1993:BRS,
author = "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
title = "On Bounding the Range of Some Elementary Functions in
{FORTRAN-77}",
journal = j-INTERVAL-COMP,
volume = "2",
number = "3(5)",
pages = "29--39",
year = "1993",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65G10",
MRnumber = "1 305 844",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "Proceedings of the International Conference on
Numerical Analysis with Automatic Result Verification
(Lafayette, LA, 1993).",
ZMnumber = "0829.65018",
abstract = "We present the techniques we have used to bound the
range of the arcsine, arccosine, arctangent,
arccotangent, and hyperbolic sine functions in our
portable FORTRAN-77 library INTLIB. The design of this
library is based on a balance of simplicity and
efficiency, subject to rigor and portability.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bounding the range; elementary functions; FORTRAN-77
library INTLIB; interval arithmetic",
xxauthor = "C. Hu and R. B. Kearfott",
}
@Misc{Hu:1993:VOI,
author = "C. Hu and R. B. Kearfott and J. Sheldon and Q. Yang",
title = "On Vectorization and Optimization of {INTBIS} on the
{Cray Y-MP}",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InProceedings{Kearfott:1993:CPG,
author = "B. Kearfott and K. Du",
title = "The cluster problem in global optimization: {The}
univariate case",
crossref = "Albrecht:1993:VNT",
volume = "9",
pages = "117--127",
year = "1993",
CODEN = "COSPDM",
ISSN = "0344-8029",
bibdate = "Sun Oct 17 11:55:48 MDT 1999",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
}
@Article{Kearfott:1993:PSH,
author = "R. Baker Kearfott and Xiaofa Shi",
title = "A preconditioner selection heuristic for efficient
iteration with decomposition of arithmetic expressions
for nonlinear algebraic systems",
journal = j-INTERVAL-COMP,
volume = "3",
number = "1",
pages = "15--33",
year = "1993",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65H10 (65G10)",
MRnumber = "1280132",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1993/interval-computations-1993-1-pp-15-33.pdf",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@Misc{Kearfott:1993:RCS,
author = "R. B. Kearfott and Z. Xing",
title = "Rigorous Computation of Surface Patch Intersection
Curves",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Novoa:1993:AIS,
author = "M. Novoa",
title = "Advances in the Interval Solution of Algebraic
Systems",
publisher = "Univ. of Southwestern Louisiana",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@PhdThesis{Xing:1993:RSC,
author = "Zh. Xing",
title = "Rigorous Step Control for Continuation",
school = "University of Southwestern Louisiana",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Yakovlev:1993:BSW,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {IV}",
journal = j-INTERVAL-COMP,
volume = "3",
number = "1",
pages = "103--115",
year = "1993",
CODEN = "????",
ISSN = "0135-4868",
MRclass = "65-00 (65G10)",
MRnumber = "1280136",
bibdate = "Sat Feb 4 18:30:48 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "Text in English and Russian.",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1993/interval-computations-1993-1-pp-103-115.pdf",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@PhdThesis{Du:1994:CPG,
author = "K. Du",
title = "Cluster Problem in Global Optimization using Interval
Arithmetic",
school = "University of Southwestern Louisiana",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Du:1994:CPM,
author = "Kaisheng Du and R. Baker Kearfott",
title = "The cluster problem in multivariate global
optimization",
journal = "J. Global Optim.",
volume = "5",
number = "3",
pages = "253--265",
year = "1994",
DOI = "https://doi.org/10.1007/BF01096455",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
MRclass = "90C30 (65G10)",
MRnumber = "1299015",
URL = "https://doi.org/10.1007/BF01096455",
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
bibdate = "Wed Oct 18 11:47:28 2023",
acknowledgement = ack-nhfb,
}
@Article{Hu:1994:GIS,
author = "C. Hu and R. B. Kearfott and Q. Yang and A. Frolov",
title = "A General Iterative Sparse Linear Solver and its
Parallelization for Interval {Newton} Methods",
journal = j-INTERVAL-COMP,
volume = "1994",
number = "4",
year = "1994",
ISSN = "0135-4868",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@Misc{Hu:1994:ISS,
author = "C. Hu and R. B. Kearfott and Q. Yang",
title = "A Indexed Storage Scheme for General Sparse Matrices
and its Applications",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Hu:1994:OIC,
author = "C. Hu and R. B. Kearfott and J. Sheldon and Q. Yang",
title = "Optimizing {INTBIS} on the {Cray Y-MP}",
journal = j-INTERVAL-COMP,
volume = "1994",
number = "4",
year = "1994",
ISSN = "0135-4868",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Interval Computations = Interval'nye vychisleniia",
}
@InProceedings{Hu:1994:SNS,
author = "C. Hu and J. Sheldon and R. B. Kearfott and Q. Yang",
booktitle = "Proc. ISCA Seventh International Conference on
Parallel and Distributed Computing Systems",
title = "Solving Nonlinear Systems on a Vector Supercomputer",
publisher = "ISCA",
pages = "832--835",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1994:AIP,
author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
title = "Algorithm 737: {INTLIB}: {A} Portable {Fortran 77}
Elementary Function Library",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "447--459",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat May 20 15:54:18 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p447-kearfott/",
ZMnumber = "0888.65057",
abstract = "INTLIB is meant to be a readily available, portable,
exhaustively documented interval arithmetic library,
written in standard Fortran 77. Its underlying
philosophy is to provide a standard for interval
operations to aid in efficiently transporting programs
involving interval arithmetic. The model is the BLAS
package, for basic linear algebra operations. The
library is composed of elementary interval arithmetic
routines, standard function routines for interval data
and values, and utility routines. The library can be
used with INTBIS (Algorithm 681), and a Fortran 90
module to use the library to define an interval data
type is available from the first author.",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic;
operator overloading; program package; standard
function routines; standard functions",
subject = "D.2.2 [Software Engineering]: Tools and Techniques --
software libraries; D.2.7 [Software Engineering]:
Distribution and Maintenance -- documentation;
portability; G.1.0 [Numerical Analysis]: General --
computer arithmetic; G.1.2 [Numerical Analysis]:
Approximation -- elementary function approximation",
}
@Article{Kearfott:1994:CPM,
author = "R. B. Kearfott and K. Du",
title = "The Cluster Problem in Multivariate Global
Optimization",
journal = j-J-GLOBAL-OPT,
volume = "5",
pages = "253--265",
year = "1994",
CODEN = "JGOPEO",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Journal of Global Optimization",
journal-URL = "http://link.springer.com/journal/10898",
}
@Misc{Kearfott:1994:EEI,
author = "R. B. Kearfott",
title = "Empirical Evaluation of Innovations in Interval Branch
and Bound Algorithms for Nonlinear Algebraic Systems",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Kearfott:1994:FSS,
author = "R. B. Kearfott and S. Ning",
title = "{FORTDIFF}: {A} Set of Subroutines for
{Fortran-to-Fortran} Differentiation of Programs",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Article{Kearfott:1994:ISC,
author = "R. Baker Kearfott and Zhaoyun Xing",
title = "An Interval Step Control for Continuation Methods",
journal = j-SIAM-J-NUMER-ANAL,
volume = "31",
number = "3",
pages = "892--914",
month = jun,
year = "1994",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G10 (65H10)",
MRnumber = "94m:65076",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Misc{Kearfott:1994:RTV,
author = "R. B. Kearfott",
title = "A Review of Techniques in the Verified Solution of
Constrained Global Optimization Problems",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Misc{Kearfott:1994:VFE,
author = "R. B. Kearfott",
title = "On Verifying Feasibility in Equality Constrained
Optimization Problems",
journal = j-MATH-PROG,
year = "1994",
CODEN = "MHPGA4",
ISSN = "0025-5610",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
}
@Misc{Shi:1994:SRR,
author = "S. Shi and R. B. Kearfott",
title = "Some Results on the Regularity of an Interval Matrix",
journal = j-COMPUTING,
year = "1994",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Yakovlev:1994:BSWa,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {V}",
journal = j-INTERVAL-COMP,
volume = "1994",
number = "1",
pages = "100--109",
year = "1994",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:03:36 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0829.65051",
acknowledgement = ack-nhfb,
classmath = "{65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis)) }",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@Article{Yakovlev:1994:BSWb,
author = "Alexander G. Yakovlev and R. Baker Kearfott",
title = "Bibliography of {Soviet} works on interval
computations. {VI}",
journal = j-INTERVAL-COMP,
volume = "1994",
number = "2",
pages = "116--126",
year = "1994",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:02:25 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0829.65052",
acknowledgement = ack-nhfb,
classmath = "65G30 (Interval and finite arithmetic) 65-00
(Reference works (numerical analysis))",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "bibliography; interval computations; Soviet works",
}
@Article{Hu:1995:GIS,
author = "Chenyi Hu and Anna Frolov and R. Baker Kearfott and
Qing Yang",
title = "A general iterative sparse linear solver and its
parallelization for interval {Newton} methods",
journal = j-RELIABLE-COMPUTING,
volume = "1",
number = "3",
pages = "251--263",
month = "????",
year = "1995",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/BF02385256",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "65G10 (65H10)",
MRnumber = "1356429",
bibdate = "Sat Jan 5 10:51:02 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=1&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1995/reliable-computing-1995-3-pp-251-263.pdf;
http://link.springer.com/article/10.1007/BF02385256;
http://link.springer.com/article/10.1007/BF02385256/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=3&spage=251-263",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Hu:1995:OIC,
author = "Chenyi Hu and Joe Sheldon and R. Baker Kearfott and
Qing Yang",
title = "Optimizing {INTBIS} on the {CRAY Y-MP}",
journal = j-RELIABLE-COMPUTING,
volume = "1",
number = "3",
pages = "265--274",
month = "????",
year = "1995",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/BF02385257",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 10:51:02 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=1&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1995/reliable-computing-1995-3-pp-265-274.pdf;
http://link.springer.com/article/10.1007/BF02385257;
http://link.springer.com/article/10.1007/BF02385257/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=3&spage=265-274",
ZMnumber = "0837.65053",
abstract = "INTBIS is a well-tested software package which uses an
interval Newton/generalized bisection method to find
all numerical solutions to systems of nonlinear
equations. Since INTBIS uses interval computations, its
results are guaranteed to contain all solutions. To
efficiently solve very large nonlinear systems on a
parallel vector computer, it is necessary to
effectively utilize the architectural features of the
machine. In this paper, we report our implementations
of INTBIS for large nonlinear systems on the Cray Y-MP
supercomputer. We first present the direct
implementation of INTBIS on a Cray. Then, we report our
work on optimizing INTBIS on the Cray Y-MP.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
classmath = "65H10 (Systems of nonlinear equations (numerical
methods)) 65G30 (Interval and finite arithmetic) 65Y05
(Parallel computation (numerical methods))",
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
keywords = "Cray Y-MP supercomputer; INTBIS; interval arithmetic;
interval Newton/generalized bisection method; parallel
computation; software package; very large nonlinear
systems",
}
@Article{Kearfott:1995:FER,
author = "R. Baker Kearfott",
title = "A {Fortran 90} Environment for Research and
Prototyping of Enclosure Algorithms for Nonlinear
Equations and Global Optimization",
journal = j-TOMS,
volume = "21",
number = "1",
pages = "63--78",
month = mar,
year = "1995",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat May 20 15:54:41 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p63-kearfott/",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "automatic differentiation; Fortran 90; global
optimization; nonlinear algebraic systems; symbolic
computation",
subject = "D.3.3 [Programming Languages]: Language Constructs;
G.1.5 [Numerical Analysis]: Roots of Nonlinear
Equations; G.1.6 [Numerical Analysis]: Optimization;
G.4 [Mathematics of Computing]: Mathematical Software",
}
@Misc{Kearfott:1995:IFM,
author = "R. B. Kearfott",
title = "{INTLIB\_ARITHMETIC}: {A} {Fortran 90} Module for an
Interval Data Type",
journal = j-TOMS,
year = "1995",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kearfott:1995:Pa,
author = "R. B. Kearfott and E. A. Musaev and V. M. Nesterov and
A. G. Yakovlev",
title = "Preface",
journal = j-RELIABLE-COMPUTING,
volume = "1",
number = "1",
pages = "3--4",
month = mar,
year = "1995",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/BF02390516",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 10:50:58 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=1&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1995/reliable-computing-1995-1-pp-3-4.pdf;
http://link.springer.com/accesspage/article/10.1007/BF02390516;
http://link.springer.com/article/10.1007/BF02390516;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=1&spage=3",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Misc{Kearfott:1995:TRI,
author = "R. B. Kearfott",
title = "Test Results for an Interval Branch and Bound
Algorithm for Equality-Constrained Optimization",
year = "1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@InCollection{Kearfott:1996:ADC,
author = "R. Baker Kearfott",
booktitle = "{Computational differentiation: techniques,
applications, and tools. Proceedings of the second
international workshop on computational
differentiation, February 12--14, 1996}",
title = "Automatic differentiation of conditional branches in
an operator overloading context",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "75--81",
year = "1996",
bibdate = "Tue Aug 24 08:14:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0940.65020",
abstract = "In the past, it has been problematical to include
IF-THEN-ELSE branches in automatic differentiation
processes driven by operator overloading and code list
generation, when the branch condition contains
variables. However, this problem can be circumvented
with a special ``branch function'' $ \chi $. Definition
of this function, formulas for its use, and
implications of its use will be discussed.\par A second
issue is: what can be done when derivatives are
discontinuous? In fact, simple an meaningful Newton
iterations can be set up when even the function itself
is discontinuous. Simplified figures and examples are
given, as well as references to in-depth explanations.
An example of the convergence behavior is given with an
interval Newton method to find critical points for the
problem ``$ \min |x| $''.",
acknowledgement = ack-nhfb,
classmath = "65D25 (Numerical differentiation) 65G30 (Interval and
finite arithmetic) 68W30 (Symbolic computation and
algebraic computation)",
keywords = "automatic differentiation; branch function;
conditional branches; convergence; discontinuous
derivatives; interval Newton method; Newton iterations;
operator overloading",
}
@Article{Kearfott:1996:AIF,
author = "R. Baker Kearfott",
title = "Algorithm 763: {INTERVAL\_ARITHMETIC}: {A Fortran 90}
Module for an Interval Data Type",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "385--392",
month = dec,
year = "1996",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "See \cite{Kearfott:1994:AIP}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p385-kearfott/",
abstract = "Interval arithmetic is useful in {\it automatically
verified computation}, that is, in computations in
which the algorithm itself rigorously proves that the
answer must lie within certain bounds. In addition to
rigor, interval arithmetic also provides a simple and
somewhat sharp method of bounding ranges of functions
for global optimization and other tasks. Convenient use
of interval arithmetic requires an interval data type
in the programming language. Although various packages
supply such a data type, previous ones are machine
specific, obsolete, and unsupported, for languages
other than Fortran, or commercial. The Fortran 90
module {INTERVAL\_ARITHMETIC} provides a portable
interval data type in Fortran 90. This data type is
based on two double-precision real Fortran storage
unit. Module {INTERVAL\_ARITHMETIC} uses the Fortran 77
library {INTLIB} (ACM TOMS Algorithm 737) as a
supporting library. The module has been employed
extensively in the author's own research.",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms, languages",
subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 90. {\bf G.1.0}: Mathematics
of Computation, NUMERICAL ANALYSIS, General, Computer
arithmetic, Error analysis, Numerical algorithms.",
}
@Article{Kearfott:1996:ICI,
author = "Baker R. Kearfott",
title = "Interval computations: introduction, uses, and
resources",
journal = j-EUROMATH-BULL,
volume = "2",
number = "1",
pages = "95--112",
year = "1996",
ISSN = "1359-4346",
MRclass = "65G10",
MRnumber = "1413179 (97g:65106)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Euromath Bulletin",
}
@Article{Kearfott:1996:IEN,
author = "R. Baker Kearfott",
title = "Interval Extensions of Non-Smooth Functions for Global
Optimization and Nonlinear Systems Solvers",
journal = j-COMPUTING,
volume = "57",
number = "2",
pages = "149--162",
month = "????",
year = "1996",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02276877",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "90C30 (65G10)",
MRnumber = "1407349 (97i:90080)",
MRreviewer = "Xiaojun Chen",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
classification = "921; 921.1; 921.5; 921.6",
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Approximation theory; Calculations; Global
optimization; Interval extensions; Newton methods; Non
smooth optimization; Nonlinear equations;
Optimization",
}
@InCollection{Kearfott:1996:OPI,
author = "R. Baker Kearfott and Xiaofa Shi",
booktitle = "{Scientific computing and validated numerics
(Wuppertal, 1995)}",
title = "Optimal preconditioners for interval {Gauss--Seidel}
methods",
volume = "90",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "173--178",
year = "1996",
MRclass = "65H10 (65F35 65G10)",
MRnumber = "1394234",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Math. Res.",
acknowledgement = ack-nhfb,
}
@Book{Kearfott:1996:RGS,
author = "R. Baker Kearfott",
title = "Rigorous global search: continuous problems",
volume = "13",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvi + 262",
year = "1996",
ISBN = "0-7923-4238-0",
ISBN-13 = "978-0-7923-4238-0",
LCCN = "QA402.5 .K388 1996",
MRclass = "90-02 (65-02 65G10 65H10 90C30)",
MRnumber = "1422659 (97i:90003)",
MRreviewer = "Svetoslav M. Markov",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Nonconvex Optimization and its Applications",
ZMnumber = "0876.90082",
acknowledgement = ack-nhfb,
}
@InCollection{Kearfott:1996:RTV,
author = "R. Baker Kearfott",
booktitle = "{Applications of interval computations (El Paso, TX,
1995)}",
title = "A review of techniques in the verified solution of
constrained global optimization problems",
volume = "3",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "23--59",
year = "1996",
MRclass = "90C30 (65G10 65K05)",
MRnumber = "1386898 (97a:90077)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Appl. Optim.",
acknowledgement = ack-nhfb,
}
@InCollection{Kearfott:1996:TNS,
author = "R. Baker Kearfott",
booktitle = "{Scientific computing and validated numerics
(Wuppertal, 1995)}",
title = "Treating non-smooth functions as smooth functions in
global optimization and nonlinear systems solvers",
volume = "90",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "160--172",
year = "1996",
MRclass = "65K05 (65G10)",
MRnumber = "1394233",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Math. Res.",
acknowledgement = ack-nhfb,
}
@InCollection{Kearfott:1996:TRI,
author = "R. Baker Kearfott",
booktitle = "{State of the art in global optimization (Princeton,
NJ, 1995)}",
title = "Test results for an interval branch and bound
algorithm for equality-constrained optimization",
volume = "7",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "181--199",
year = "1996",
MRclass = "90C30 (65G10)",
MRnumber = "1390533",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Nonconvex Optim. Appl.",
acknowledgement = ack-nhfb,
}
@Article{Kirfott:1995:PRF,
author = "R. B. Kirfott and Je. A. Musaev and V. M. Nesmerov and
A. G. Jakovlev",
title = "Predislovie. ({Russian}) [{Foreword}]",
journal = j-RELIABLE-COMPUTING,
volume = "1",
number = "1",
pages = "5--7",
month = "????",
year = "1995",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/BF02390517",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 10:50:58 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=1&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://interval.louisiana.edu/reliable-computing-journal/1995/reliable-computing-1995-1-pp-5-7.pdf;
http://link.springer.com/article/10.1007/BF02390517;
http://link.springer.com/article/10.1007/BF02390517/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=1&spage=5-7",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
language = "Russian",
}
@InCollection{Rocha:1996:CUI,
author = "Luis Mateus Rocha and Vladik Kreinovich and R. Baker
Kearfott",
booktitle = "{Applications of interval computations (El Paso, TX,
1995)}",
title = "Computing uncertainty in interval based sets",
volume = "3",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "337--380",
year = "1996",
MRclass = "65G10 (04A72)",
MRnumber = "1386909 (97a:65048)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Appl. Optim.",
acknowledgement = ack-nhfb,
}
@Article{Kearfott:1997:EEI,
author = "R. Baker Kearfott",
title = "Empirical Evaluation of Innovations in Interval Branch
and Bound Algorithms for Nonlinear Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "18",
number = "2",
pages = "574--594",
month = mar,
year = "1997",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827594266131",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G10 (65H20); 65G10 (65Hxx)",
MRnumber = "1433796 (97m:65094)",
MRreviewer = "J. Michel Muller",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0871.65042",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Ning:1997:CSM,
author = "S. Ning and R. B. Kearfott",
title = "A Comparison of Some Methods for Solving Linear
Interval Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "34",
number = "4",
pages = "1289--1305",
month = aug,
year = "1997",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/S0036142994270995",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G10 (65F05)",
MRnumber = "1461785 (98m:65081)",
MRreviewer = "H. Ratschek",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://epubs.siam.org:80/sam-bin/dbq/toclist/SINUM",
ZMnumber = "0889.65022",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Kearfott:1998:BRK,
author = "R. Baker Kearfott",
title = "Book Review: {Kreinovich, V., Lakeyev, A., Rohn, J.,
and Kahl, P.: \booktitle{Computational Complexity and
Feasibility of Data Processing and Interval
Computations}}",
journal = j-RELIABLE-COMPUTING,
volume = "4",
number = "4",
pages = "405--409",
month = nov,
year = "1998",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1024484203503",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:00:51 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=4&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "See \cite{Kreinovich:1998:CCF}.",
URL = "http://link.springer.com/article/10.1023/A%3A1024484203503/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=4&issue=4&spage=405;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=4&issue=4&spage=405-409",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:1998:BRN,
author = "R. Baker Kearfott",
title = "Book Reviews: {{\em Numerica: A modelling language for
global optimization}}, by {Pascal Van Hentenryck},
{Laurent Michel}, and {Yves Deville}",
journal = j-MATH-COMPUT,
volume = "67",
number = "224",
pages = "??--??",
month = oct,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Jul 26 12:37:20 1999",
bibsource = "http://www.ams.org/mcom/1998-67-224;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00989-2&u=/mcom/1998-67-224/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
xxpages = "1739--1751",
}
@Article{Kearfott:1998:PEF,
author = "R. Baker Kearfott",
title = "On proving existence of feasible points in equality
constrained optimization problems",
journal = j-MATH-PROG,
volume = "83",
number = "1, Ser. A",
pages = "89--100",
year = "1998",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1016/S0025-5610(97)00107-X",
ISSN = "0025-5610",
MRclass = "90C30 (65G10 65K05)",
MRnumber = "1643955 (99i:90085)",
MRreviewer = "H. Ratschek",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0949.90089",
abstract = "Various algorithms can compute approximate feasible
points or approximate solutions to equality and bound
constrained optimization problems. In exhaustive search
algorithms for global optimizers and other contexts, it
is of interest to construct bounds around such
approximate feasible points, then to verify
(computationally but rigorously) that an actual
feasible point exists within these bounds. Hansen and
others have proposed techniques for proving the
existence of feasible points within given bounds, but
practical implementations have not, to our knowledge,
previously been described. Various alternatives are
possible in such an implementation, and details must be
carefully considered. Also, in addition to Hansen's
technique for handling the underdetermined case, it is
important to handle the overdetermined case, when the
approximate feasible point corresponds to a point with
many active bound constraints. The basic ideas, along
with experimental results from an actual
implementation, are summarized here.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
}
@Article{Kearfott:1998:RGS,
author = "R. Baker Kearfott and Eldon Hansen",
title = "Rigorous Global Search: Continuous Problems",
journal = j-SIAM-REVIEW,
volume = "40",
number = "1",
pages = "153--??",
month = "????",
year = "1998",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Apr 9 08:47:36 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@InCollection{Corliss:1999:RGS,
author = "George F. Corliss and R. Baker Kearfott",
booktitle = "{Developments in reliable computing. SCAN-98
conference, 8th international symposium on Scientific
computing, computer arithmetic and validated numerics.
Budapest, Hungary, September 22--25, 1998}",
title = "Rigorous global search: Industrial applications",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "1--16",
year = "1999",
bibdate = "Tue Aug 24 08:19:17 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "0949.65067",
abstract = "{Summary: We apply interval techniques for global
optimization to several industrial applications
including Swiss Bank (currency trading), BancOne
(portfolio management), MacNeal-Schwendler (finite
element), GE Medical Systems (Magnetic resonance
imaging), Genome Therapeutics (gene prediction),
inexact greatest common divisor computations from
computer algebra, and signal processing. We describe
each of the applications, discuss the solutions
computed by Kearfott's GlobSol software (see
www.mscs.mu.edu/$ \sim $ globsol), and tell of the
lessons learned. In each of these problems, GlobSol's
rigorous global optimization provided significant new
insights to us and to our industrial partners.}",
acknowledgement = ack-nhfb,
classmath = "{65K05 (Mathematical programming (numerical methods))
65Y15 (Packaged methods in numerical analysis) 90C30
(Nonlinear programming) 90C90 (Applications of
mathematical programming) }",
keywords = "computer algebra; currency trading; finite element
analysis; gene prediction; global optimization; GlobSol
software; industrial applications; least common
denominator; magnetic resonance imaging; portfolio
management; signal processing",
}
@TechReport{Kearfott:1999:SCV,
author = "R. Baker Kearfott",
title = "On Stopping Criteria in Verified Nonlinear Systems or
Optimization Algorithms",
institution = "University of Louisiana",
address = "New Orleans, LA, USA",
pages = "????",
year = "1999",
bibdate = "Mon Oct 04 10:07:13 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://interval.usl.edu/preprints/TOMS_thick.ps",
acknowledgement = ack-nhfb,
}
@Article{Kearfott:2000:EVS,
author = "R. Baker Kearfott and Jianwei Dian and A. Neumaier",
title = "Existence verification for singular zeros of complex
nonlinear systems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "38",
number = "2",
pages = "360--379",
year = "2000",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/S0036142999361074",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G30; 65H10 [ Systems of nonlinear equations
(numerical methods)]; 30C15 [ Zeros of polynomials,
etc. (one complex variable)]; 65E05 [Numerical methods
in complex analysis]; 55M25 [Degree, winding number]",
MRnumber = "1770053 (2001e:65078)",
MRreviewer = "H. Ratschek",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
abstract = "There exists a wide spectrum of methods for solving $
F(x) = 0 $, where $F$ is a nonlinear function $ \mathbb
{R} n \rightarrow \mathbb {R} n$. Fixed point theorems
in conjunction with interval-analysis can be used to
automatically verify existence and uniqueness of a
solution within a given region $D$. Most methods,
however, succeed only when the Jacobian of $F$ is
regular in $D$. In problems such as bifurcation or
surface intersection, the Jacobian may be singular or
ill-conditioned at the desired solution. In such cases,
arbitrarily small perturbations of $F$ can lead to no
solution or many solutions in $D$.\par
The present paper provides a special-purpose tool for
singular Jacobians in cases where $F$ can be extended
to an analytic function $ \mathbb {C}^n \rightarrow
\mathbb {C}^n$. Existence verification is possible by
computing the topological degree of $F$ with respect to
a prescribed region. The notion topological degree
generalizes the sign-change of a one-dimensional real
function and the winding-number of an analytic
function. The topological degree gives the number of
solutions of $ F(z) = 0$, counting multiplicities,
within a region in $ \mathbb {C}^n$. The authors
describe in detail how to compute the topological
degree of $F$ with respect to a box in $ \mathbb
{C}^n$. Hereby a sophisticated organization reduces the
amount of work considerably, compared to previously
known methods. Numerical examples illustrate the
efficiency of the presented algorithm.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Kearfott:2000:SCV,
author = "R. B. Kearfott and G. W. Walster",
title = "On stopping criteria in verified nonlinear systems or
optimization algorithms",
journal = j-TOMS,
volume = "26",
number = "3",
pages = "373--389",
year = "2000",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/358407.358418",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G20 (65H10 90C30)",
MRnumber = "1809949 (2001i:65058)",
MRreviewer = "K. Schittkowski",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Association for Computing Machinery. Transactions on
Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Kearfott:2001:ESN,
author = "R. Baker Kearfott",
title = "An example of singularity in nonlinear systems",
journal = j-RELIABLE-COMPUTING,
volume = "7",
number = "5",
pages = "425--429",
month = oct,
year = "2001",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1011484228528",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "90C30 (65K10 90C57)",
MRnumber = "1862923 (2002g:90102)",
bibdate = "Sat Jan 5 16:01:32 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=7&issue=5;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1011484228528/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=7&issue=5&spage=425;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=7&issue=5&spage=425-429",
abstract = "Certain practical constrained global optimization
problems have to date defied practical solution with
interval branch-and-bound methods. The exact mechanism
causing the difficulty has been difficult to pinpoint.
Here, an example is given where the equality constraint
set has higher-order singularities and degenerate
manifolds of singularities on the feasible set. The
reason that this causes problems is discussed, and ways
of fixing it are suggested.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2002:EUV,
author = "R. Baker Kearfott",
title = "On Existence and Uniqueness Verification for
Non-Smooth Functions",
journal = j-RELIABLE-COMPUTING,
volume = "8",
number = "4",
pages = "267--282",
month = aug,
year = "2002",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1016381031155",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "65H10 (65G40)",
MRnumber = "1914594 (2003h:65066)",
MRreviewer = "Ljiljana Petkovi{\'c}",
bibdate = "Sat Jan 5 16:01:44 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=8&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1016381031155/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=4&spage=267;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=4&spage=267-282",
ZMnumber = "0999.65041",
abstract = "Given an approximate solution to a nonlinear system of
equations at which the Jacobi matrix is nonsingular,
and given that the Jacobi matrix is continuous in a
region about this approximate solution, a small box can
be constructed about the approximate solution in which
interval Newton methods can verify existence and
uniqueness of an actual solution.\par
Recently, we have shown how to verify existence and
uniqueness, up to multiplicity, for solutions at which
the Jacobi matrix is singular. We do this by efficient
computation of the topological index over a small box
containing the approximate solution. Since the
topological index is defined and computable when the
Jacobi matrix is not even defined at the solution, one
may speculate that efficient algorithms can be devised
for verification in this case, too.\par
In this note, however, we discuss, through examples,
key techniques underlying our simplification of the
calculations that cannot necessarily be used when the
function is non-smooth. We also present those parts of
the theory that are valid in the non-smooth case, and
suggest when degree computations involving non-smooth
functions may be practical.\par
As a bonus, the examples lead to additional
understanding of previously published work on
verification involving the topological degree.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2002:SCO,
author = "R. Baker Kearfott and G. William Walster",
title = "{SIAM} Conference on Optimization, Validated Computing
2002, and the Fields Institute Informal Working Group
on Validated Optimization",
journal = j-RELIABLE-COMPUTING,
volume = "8",
number = "5",
pages = "419--424",
month = oct,
year = "2002",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1020583804772",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:01:46 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=8&issue=5;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1020583804772/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=5&spage=419;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=5&spage=419-424",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2002:SPT,
author = "R. Baker Kearfott and G. William Walster",
title = "Symbolic Preconditioning with {Taylor} Models: Some
Examples",
journal = j-RELIABLE-COMPUTING,
volume = "8",
number = "6",
pages = "453--468",
month = dec,
year = "2002",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1021364526413",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "65G30 (90C30)",
MRnumber = "1943231 (2003m:65068)",
bibdate = "Sat Jan 5 16:01:49 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=8&issue=6;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1021364526413/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=6&spage=453;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=6&spage=453-468",
ZMnumber = "1016.65041",
abstract = "Deterministic global optimization with interval
analysis involves \par
-- using interval enclosures for ranges of the
constraints, objective, and gradient to reject
infeasible regions, regions without global optima, and
regions without critical points; \par
-- using interval Newton methods to converge on
optimum-containing regions and to verify global optima.
\par
There are certain problems for which interval
dependency leads to overestimation in the enclosures of
the individual components, causing the optimization
search to become prohibitively inefficient. As {\it E.
R. Hansen} has observed earlier [Computing 58, No. 2,
187-196 (1997; Zbl 0918.65037)], in other problems,
there is no overestimation in the individual
components, but overestimation is introduced in the
preconditioning in the interval Newton method. \par
We examine these issues for a particular nonlinear
systems problem that, to date, has defied numerical
solution. To reduce overestimation, we use Taylor
models. The Taylor models sometimes reduce individual
overestimation but, consistent with Hansen's
observations, especially reduce the overestimation due
to preconditioning. From numerical experiments, we
conclude that, in certain instances, Taylor models can
greatly reduce both the number of subregions necessary
to complete an exhaustive search and the total
computational effort.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2002:VTI,
author = "R. Baker Kearfott and Jianwei Dian",
title = "Verifying topological indices for higher-order rank
deficiencies",
journal = j-J-COMPLEXITY,
volume = "18",
number = "2",
pages = "589--611",
year = "2002",
CODEN = "JOCOEH",
DOI = "https://doi.org/10.1006/jcom.2001.0634",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
MRclass = "65H10 (65G20)",
MRnumber = "1919451 (2003g:65068)",
MRreviewer = "B. Kellogg",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Algorithms and complexity for continuous
problems/Algorithms, computational complexity, and
models of computation for nonlinear and multivariate
problems (Dagstuhl/South Hadley, MA, 2000)",
ZMnumber = "1005.65049",
abstract = "It has been known how to use computational fixed point
theorems to verify existence and uniqueness of a true
solution to a system of nonlinear equations within a
small region about an approximate solution. This can,
be done in $ O(n^3) $ operations, where $n$ is the
number of equations and unknowns. However, these
standard techniques are only valid if the Jacobi matrix
for the system is nonsingular at the solution.\par
In previous work and a dissertation (of Dian), we have
shown, both theoretically and practically, that
existence and multiplicity can be verified in a complex
setting, and in the real setting for odd multiplicity,
when the rank defect of the Jacobi matrix at an
isolated solution is $1$. Here, after reviewing work to
date, we discuss the case of higher rank defect. In
particular, it appears that $p$-dimensional searches
are required if the rank defect is $p$, and that the
work increases exponentially in $p$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Complexity",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
}
@Article{Dian:2003:EVS,
author = "Jianwei Dian and R. Baker Kearfott",
title = "Existence verification for singular and nonsmooth
zeros of real nonlinear systems",
journal = j-MATH-COMPUT,
volume = "72",
number = "242",
pages = "757--766",
year = "2003",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-02-01427-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G20 (65H10)",
MRnumber = "1954966 (2004a:65056)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kearfott:2003:CWG,
author = "R. Baker Kearfott",
title = "{COCOS'02 --- A Workshop on Global Constrained
Optimization and Constraint Satisfaction October 2--4,
2002, Sophia-Antipolis, France}",
journal = j-RELIABLE-COMPUTING,
volume = "9",
number = "1",
pages = "81--87",
month = feb,
year = "2003",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1023014011858",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:01:52 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=9&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1023014011858/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=9&issue=1&spage=81;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=9&issue=1&spage=81-87",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2003:DCa,
author = "R. Baker Kearfott",
title = "Dear colleagues",
journal = j-RELIABLE-COMPUTING,
volume = "9",
number = "2",
pages = "89--90",
month = apr,
year = "2003",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1023022731988",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:01:54 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=9&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/accesspage/article/10.1023/A%3A1023022731988;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=9&issue=2&spage=89;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=9&issue=2&spage=89-90",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2003:DCb,
author = "R. Baker Kearfott",
title = "Dear colleagues",
journal = j-RELIABLE-COMPUTING,
volume = "9",
number = "5",
pages = "315--315",
month = oct,
year = "2003",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1025127211629",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=9&issue=5;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/accesspage/article/10.1023/A%3A1025127211629;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=9&issue=5&spage=315",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2003:EVH,
author = "R. Baker Kearfott and Jianwei Dian",
title = "Existence verification for higher degree singular
zeros of nonlinear systems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "41",
number = "6",
pages = "2350--2373",
year = "2003",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/S0036142901386057",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65H10",
MRnumber = "2034619 (2004i:65045)",
MRreviewer = "M. A. Wolfe",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1059.65045",
abstract = "Finding approximate solutions to systems of $n$
nonlinear equations in $n$ real variables is a much
studied problem in numerical analysis. Somewhat more
recently, researchers have developed numerical methods
to provide mathematically rigorous error bounds on such
solutions. (We say that we ``verify'' existence of the
solution within those bounds on the variables.)
However, when the Jacobi matrix is singular at the
solution, no computational techniques to verify
existence can handle the general case. Nonetheless,
computational verification that one or more solutions
exists within a region in complex space containing the
real bounds is possible by computing the topological
degree.\par
In a previous paper, we presented theory and algorithms
for the simplest case, when the rank-defect of the
Jacobian matrix at the solution is 1 and the
topological index is 2 [cf. {\it R. B. Kearfott, J.
Dian}, and {\it A. Neumaier}, ibid. 38, No. 2, 360--379
(2000; Zbl 0986.65054)]. Here, we generalize that
result to arbitrary topological index $ d \ge 2$: We
present theory, algorithms, and experimental results.
We also present a heuristic for determining the degree,
obtaining a value that we can subsequently verify with
our algorithms. Although execution times are slow
compared to corresponding bound verification processes
for nonsingular systems, the order with respect to
system size is still cubic.",
acknowledgement = ack-nhfb,
classmath = "{65H10 (Systems of nonlinear equations (numerical
methods)) 65G20 (Algorithms with automatic result
verification) 65G30 (Interval and finite arithmetic)
65E05 (Numerical methods in complex analysis) }",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "algorithm; complex nonlinear systems; interval
computations; numerical examples; singularities;
topological degree; verified computations",
}
@InCollection{Kearfott:2003:GHC,
author = "R. Baker Kearfott",
editor = "Christian Bliek and others",
booktitle = "{Global optimization and constraint satisfaction.
First international workshop on global constraint
optimization and constraint satisfaction, COCOS 2002,
Valbonne-Sophia Antipolis, France, October 2 -4,
2002}",
title = "{GlobSol}: History, composition, and advice on use",
publisher = pub-SV,
address = pub-SV:adr,
year = "2003",
DOI = "https://doi.org/10.1007/b94062",
bibdate = "Tue Aug 24 08:30:55 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
abstract = "The GlobSol software package combines various ideas
from interval analysis, automatic differentiation, and
constraint propagation to provide verified solutions to
unconstrained and constrained global optimization
problems. After briefly reviewing some of these
techniques and GlobSol's development history, we
provide the first overall description of GlobSol's
algorithm. Giving advice on use, we point out strengths
and weaknesses in GlobSol's approaches. Through
examples, we show how to configure and use GlobSol.",
acknowledgement = ack-nhfb,
classmath = "{68T20 (AI problem solving (heuristics, search
strategies, etc.)) 90C59 (Approximation methods and
heuristics) }",
keywords = "automatic differentiation; constraint propagation;
GlobSol; interval analysis; verified global
optimization",
}
@Article{Kearfott:2003:SIP,
author = "R. Baker Kearfott",
title = "{Special issue: Proceedings of the validated computing
2002 conference, Toronto, Canada, May 23--25, 2002}",
journal = j-RELIABLE-COMPUTING,
volume = "9",
number = "5",
pages = "315--316",
month = oct,
year = "2003",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1025127211629",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Tue Aug 24 08:33:44 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A:1025127211629",
ZMnumber = "1039.65500",
acknowledgement = ack-nhfb,
classmath = "{65-06 (Proceedings of conferences (numerical
analysis)) 00B25 (Proceedings of conferences of
miscellaneous specific interest) }",
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@InCollection{Kearfott:2004:LTI,
author = "R. Baker Kearfott and Markus Neher and Shin'ichi Oishi
and Fabien Rico",
title = "Libraries, tools, and interactive systems for verified
computations four case studies",
crossref = "Alt:2004:NSR",
year = "2004",
DOI = "https://doi.org/10.1007/b96498",
bibdate = "Tue Aug 24 08:39:43 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1126.65329",
abstract = "As interval analysis-based reliable computations find
wider application, more software is becoming available.
Simultaneously, the applications for which this
software is designed are becoming more diverse. Because
of this, the software itself takes diverse forms,
ranging from libraries for application development to
fully interactive systems. The target applications
range from fairly general to specialized.\par
Here, we describe the design of four freely available
software systems providing validated computations.
Oishi provides Slab, a complete, high-performance
system for validated linear algebra whose user
interface mimics both Matlab's M-files and a large
subset of Matlab's command-line functions. In contrast,
CADNA (Fabien Rico) is a C++ library designed to give
developers of embedded systems access to validated
numeric computations. Addressing global constrained
optimization and validated solution of nonlinear
algebraic systems, Kearfott's GlobSol focuses on
providing the most practical such system possible
without specifying non-general problem structure;
Kearfott's system has a Fortran-90 interface. Finally,
Neher provides a mathematically sound stand-alone
package ACETAF with an intuitive graphical user
interface for computing complex Taylor coefficients and
their bounds, radii of convergence, etc.\par
Overviews of each package's capabilities, use, and
instructions for obtaining and installing appear.",
acknowledgement = ack-nhfb,
classmath = "{65Y15 (Packaged methods in numerical analysis) 65G20
(Algorithms with automatic result verification) }",
keywords = "embedded systems; global optimization; interactive
software systems; interval arithmetic; numerical linear
algebra; software libraries; stochastic arithmetic;
Taylor series; Validated computations",
}
@Article{Munoz:2004:SIG,
author = "Humberto Mu{\~n}oz and R. Baker Kearfott",
title = "Slope Intervals, Generalized Gradients, Semigradients,
Slant Derivatives, and {Csets}",
journal = j-RELIABLE-COMPUTING,
volume = "10",
number = "3",
pages = "163--193",
month = jun,
year = "2004",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/B:REOM.0000032107.85627.45",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "49J52 (65K05 90C56)",
MRnumber = "2057874 (2005f:49047)",
MRreviewer = "G{\'e}rard Lebourg",
bibdate = "Sat Jan 5 16:02:12 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/B%3AREOM.0000032107.85627.45/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=3&spage=163;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=3&spage=163-193",
ZMnumber = "1072.65094",
abstract = "In classical optimization problems for smooth
functions, automatic differentiation techniques are
often used to provide gradients for descent algorithms.
These can be combined with interval arithmetic ideas to
obtain enclosures for gradients. For nonsmooth
optimization problems, gradients are often replaced by
slopes, semigradients, generalized gradients and slant
derivatives. However it is not clear in general how to
adapt the techniques of automatic differentiation and
interval analysis to compute these quantities (with the
exception of interval slopes, for which a calculus is
available and automatic differentiation ideas can be
used).\par
This paper examines the relationship between these
different approaches to non-smooth optimization, in
particular when one-sided derivatives exist. Theorems
can be proved and valid enclosures calculated for these
cases.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
classmath = "65K10 (Optimization techniques (numerical methods))
49J52 (Nonsmooth analysis (other weak concepts of
optimality)) 65G40 (General methods in interval
analysis) 49M25 (Discrete approximations in calculus of
variations)",
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
keywords = "automatic differentiation; csets; descent algorithms;
generalized gradients; interval analysis; non-smooth
optimization problems; semigradients; slant
derivatives; slope intervals",
reviewer = "Marco Marletta (Cardiff)",
xxnumber = "3",
xxvolume = "4",
}
@Article{Kearfott:2005:EOI,
author = "R. Baker Kearfott",
title = "Errata and opinion to: {``An interval entropy penalty
method for nonlinear global optimization'' [Reliab.
Comput. {\bf 4}(1) (1998), 15--25; MR1617525] by
Zhengyu Huang}",
journal = j-RELIABLE-COMPUTING,
volume = "11",
number = "2",
pages = "163--164",
month = apr,
year = "2005",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/s11155-005-3035-3",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "90C30 (65K05)",
MRnumber = "2147805",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=11&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "See \cite{Huang:1998:IEP}.",
URL = "http://link.springer.com/accesspage/article/10.1007/s11155-005-3035-3;
http://link.springer.com/article/10.1007/s11155-005-3035-3;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=11&issue=2&spage=163;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=11&issue=2&spage=163-164",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2005:VCS,
author = "R. Baker Kearfott",
title = "Validated Constraint Solving --- Practicalities,
Pitfalls, and New Developments",
journal = j-RELIABLE-COMPUTING,
volume = "11",
number = "5",
pages = "383--391",
month = oct,
year = "2005",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/s11155-005-0045-0",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "90C30 (65K10)",
MRnumber = "2145173 (2006c:90083)",
bibdate = "Sat Jan 5 16:02:32 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=11&issue=5;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1007/s11155-005-0045-0;
http://link.springer.com/article/10.1007/s11155-005-0045-0/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=11&issue=5&spage=383;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=11&issue=5&spage=383-391",
ZMnumber = "1081.65526",
abstract = "Many constraint propagation techniques iterate through
the constraints in a straightforward manner, but can
fail because they do not take account of the coupling
between the constraints.However, some methods of taking
account of this coupling are local in nature, and fail
if the initial search region is too large.We put into
perspective newer methods, based on linear relaxations,
that can often replace brute-force search with the
solution of a large, sparse linear
program.\par
Robustness has been recognized as important in
geometric computations and elsewhere for at least a
decade, and more and more developers are including
validation in the design of their systems. We provide
citations to our work and to the work of others to-date
in developing validated versions of linear
relaxations.\par
This work is in the form of a brief review and
prospectus for future development. We give various
simple examples to illustrate our points.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
keywords = "geometric computations; large, sparse linear program;
linear relaxations; robustness",
}
@Article{Kearfott:2005:VLR,
author = "R. Baker Kearfott and Siriporn Hongthong",
title = "Validated linear relaxations and preprocessing: some
experiments",
journal = j-SIAM-J-OPT,
volume = "16",
number = "2",
pages = "418--433",
year = "2005",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/030602186",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C30 (65G20 65K10 68Q25 90C26)",
MRnumber = "2197988 (2006m:90160)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1122.90075",
abstract = "Based on work originating in the early 1970s, a number
of recent global optimization algorithms have relied on
replacing an original nonconvex nonlinear program by
convex or linear relaxations. Such linear relaxations
can be generated automatically through an automatic
differentiation process. This process decomposes the
objective and constraints (if any) into convex and
nonconvex unary and binary operations. The convex
operations can be approximated arbitrarily well by
appending additional constraints, while the domain must
somehow be subdivided (in an overall branch-and-bound
process or in some other local process) to handle
nonconvex constraints. In general, a problem can be
hard if even a single nonconvex term appears. However,
certain nonconvex terms lead to easier-to-solve
problems than others. Recently, Neumaier, Lebbah,
Michel, ourselves, and others have paved the way to
utilizing such techniques in a validated
context.\par
In this paper, we present a symbolic preprocessing step
that provides a measure of the intrinsic difficulty of
a problem. Based on this step, one of two methods can
be chosen to relax nonconvex terms. This preprocessing
step is similar to a method previously proposed by {\it
T. G. W. Epperly} and {\it E. N. Pistikopoulos} [J.
Glob. Optim. 11, No. 3, 287--311 (1997; Zbl
1040.90567)] for determining subspaces in which to
branch, but we present it from a different point of
view that is amenable to simplification of the problem
presented to the linear programming solver, and within
a validated context. Besides an illustrative example,
we have implemented general relaxations in a validated
context, as well as the preprocessing technique, and we
present experiments on a standard test set. Finally, we
present conclusions.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
keywords = "automatic differentiation; computational complexity;
global optimization; GlobSol; linear relaxation;
nonconvex optimization; symbolic computation",
}
@Article{Kreinovich:2005:BCG,
author = "Vladik Kreinovich and R. Baker Kearfott",
title = "Beyond convex? {Global} optimization is feasible only
for convex objective functions: a theorem",
journal = j-J-GLOBAL-OPT,
volume = "33",
number = "4",
pages = "617--624",
year = "2005",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-004-2120-1",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
MRclass = "90C25 (68Q17 90C26 90C60)",
MRnumber = "2190763 (2006g:90084)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1097.90071",
abstract = "It is known that there are feasible algorithms for
minimizing convex functions, and that for general
functions, global minimization is a difficult (NP-hard)
problem. It is reasonable to ask whether there exists a
class of functions that is larger than the class of all
convex functions for which we can still solve the
corresponding minimization problems feasibly. In this
paper, we prove, in essence, that no such more general
class exists. In other words, we prove that global
optimization is always feasible only for convex
objective functions.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
keywords = "Computational complexity; Global optimization;
Non-convexity",
}
@Article{Kearfott:2006:DEC,
author = "R. Baker Kearfott",
title = "Discussion and empirical comparisons of linear
relaxations and alternate techniques in validated
deterministic global optimization",
journal = j-OPTIM-METHODS-SOFTW,
volume = "21",
number = "5",
pages = "715--731",
year = "2006",
DOI = "https://doi.org/10.1080/10556780500130525",
ISSN = "1055-6788",
ISSN-L = "1026-7670",
MRclass = "90C30 (65G40)",
MRnumber = "2238654 (2007e:90104)",
MRreviewer = "Uwe Sch{\"a}fer",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1112.90080",
abstract = "Both theory and implementations in deterministic
global optimization have advanced significantly in the
past decade. Two schools of thought have developed: the
first employs various bounding techniques without
validation, while the second employs different
techniques, in a way that always rigorously takes
account of roundoff error (i.e. with validation).
However, convex relaxations, until very recently used
without validation, can be implemented efficiently in a
validated context. Here, we empirically compare a
validated implementation of a variant of convex
relaxations (linear relaxations applied to each
intermediate operation) with traditional techniques
from validated global optimization (interval constraint
propagation and interval Newton methods). Experimental
results show that linear relaxations are of significant
value in validated global optimization, although
further exploration will probably lead to more
effective inclusion of the technology.",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
}
@Article{Corliss:2007:FRA,
author = "George Corliss and Christopher Foley and R. Baker
Kearfott",
title = "Formulation for Reliable Analysis of Structural
Frames",
journal = j-RELIABLE-COMPUTING,
volume = "13",
number = "2",
pages = "125--147",
month = apr,
year = "2007",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1007/s11155-006-9027-0",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 15:48:24 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=13&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1007/s11155-006-9027-0;
http://link.springer.com/article/10.1007/s11155-006-9027-0/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=13&issue=2&spage=125;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=13&issue=2&spage=125-147",
ZMnumber = "1106.74040",
abstract = "Structural engineers use design codes formulated to
consider uncertainty for both reinforced concrete and
structural steel design. For a simple one-bay
structural steel frame, we survey typical uncertainties
and compute an interval solution for displacements and
forces. The naive solutions have large
over-estimations, so we explore Mullen-Muhanna assembly
strategy, scaling, and constraint propagation to
achieve tight enclosures of the true ranges for
displacements and forces in a fraction of CPU time
typically used for simulations. That we compute tight
enclosures, even for large parameter uncertainties used
in practice, suggests the promise of interval methods
for much larger structures.",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
classmath = "74K99 (Thin bodies, structures (solid mechanics))
74S30 (Other numerical methods in solid mechanics)
62N05 (Reliability and life testing (survival
analysis)) 65G30 (Interval and finite arithmetic)",
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
keywords = "interval arithmetic; Mullen-Muhanna assembly; one-bay
structural steel frame; uncertainty",
}
@InCollection{Corliss:2008:ISL,
author = "George F. Corliss and R. Baker Kearfott and Ned
Nedialkov and John D. Pryce and Spencer Smith",
booktitle = "{Reliable implementation of real number algorithms:
Theory and practice. International seminar, Dagstuhl
Castle, Germany, January 8--13, 2006. Revised papers}",
title = "Interval subroutine library mission",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "ix + 237",
pages = "??--??",
year = "2008",
DOI = "https://doi.org/10.1007/978-3-540-85521-7_2",
ISBN = "3-540-85520-3 (paperback)",
ISBN-13 = "978-3-540-85520-0 (paperback)",
LCCN = "QA76.95 .R45 2008",
bibdate = "Tue Aug 24 08:51:58 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1165.65407",
abstract = "We propose the collection, standardization, and
distribution of a full-featured, production quality
library for reliable scientific computing with routines
using interval techniques for use by the wide community
of applications developers.",
acknowledgement = ack-nhfb,
classmath = "65Y99 (Computer aspects of numerical algorithms) 65G30
(Interval and finite arithmetic)",
}
@InCollection{Hu:2008:IMK,
author = "Chenyi Hu and R. Baker Kearfott",
title = "Interval Matrices in Knowledge Discovery",
crossref = "Hu:2008:KPI",
pages = "98--118",
year = "2008",
bibdate = "Wed Nov 26 12:53:45 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
}
@Article{Kearfott:2008:CSM,
author = "R. B. Kearfott",
title = "A comparison of some methods for bounding connected
and disconnected solution sets of interval linear
systems",
journal = j-COMPUTING,
volume = "82",
number = "1",
pages = "77--102",
year = "2008",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-008-0258-2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G40 (65F10 65K99)",
MRnumber = "2395269 (2009c:65107)",
MRreviewer = "Ljiljana Petkovi{\'c}",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
ZMnumber = "1180.65055",
abstract = "The paper focuses on the preconditioned interval
Gauss--Seidel method for enclosing the set of all
solutions of linear systems $ Y \, A x = Y b $, where $
A, b $ are allowed to vary in a given interval matrix $
{\bold A} = [\underline A, \overline A] $ and a
corresponding interval vector $ {\bold b} $,
respectively; $Y$ is a preconditioning point matrix
used to reduce the width of overestimation of the
unpreconditioned method. The preconditioner can even be
chosen such that zero is contained in some of the
diagonal entries of $ Y{\bold A}$ leading to
disconnected semi-infinite components of the
Gauss--Seidel iterate. Such preconditioners are called
splitting- or $S$-preconditioners. Optimization
problems are formulated for special representatives of
them and for various other preconditioners which are
optimal in a specific sense. Based on detailed studies
of numerous examples two composite polynomial time
algorithms are proposed which incorporate all of these
preconditioners. The algorithms were tested with
randomly generated matrices, as well as with selected
matrices from the Matrix Market collection. It turns
out that in many cases the traditional inverse midpoint
preconditioner $ Y = ((\underline A + \overline A) /
2)^{-1}$ is inferior to the new choices of $Y$.",
acknowledgement = ack-nhfb,
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "disconnected solution set; extended intervals;
interval Gauss--Seidel method; interval linear systems;
preconditioner; preconditioning",
reviewer = "M. Milla Miranda (Rio de Janeiro)",
}
@InCollection{Kearfott:2008:FIC,
author = "Ralph Baker Kearfott and Chenyi Hu",
title = "Fundamentals of Interval Computing",
crossref = "Hu:2008:KPI",
pages = "??--??",
year = "2008",
bibdate = "Wed Nov 26 12:53:45 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
}
@Article{Bialecki:2009:GEP,
author = "Bernard Bialecki and Baker R. Kearfott and Krzysztof
A. Sikorski and Masaki Sugihara",
title = "Guest editors' preface: issue dedicated to {Professor
Frank Stenger}",
journal = j-J-COMPLEXITY,
volume = "25",
number = "3",
pages = "233--236",
year = "2009",
CODEN = "JOCOEH",
DOI = "https://doi.org/10.1016/j.jco.2009.02.002",
ISSN = "0885-064X (print), 1090-2708 (electronic)",
ISSN-L = "0885-064X",
MRclass = "41-06",
MRnumber = "2524544",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Complexity",
journal-URL = "http://www.sciencedirect.com/science/journal/0885064X",
}
@Article{Kearfott:2009:GUG,
author = "R. Baker Kearfott",
title = "{GlobSol} user guide",
journal = j-OPTIM-METHODS-SOFTW,
volume = "24",
number = "4-5",
pages = "687--708",
year = "2009",
DOI = "https://doi.org/10.1080/10556780802614051",
ISSN = "1055-6788",
ISSN-L = "1026-7670",
MRclass = "90C30 (65K10 90-08 90C26)",
MRnumber = "2554906 (2010i:90116)",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
abstract = "We explain the installation and use of the GlobSol
package for mathematically rigorous bounds on all
solutions to constrained and unconstrained global
optimization problems, as well as non-linear systems of
equations. This document should be of use both to
people with optimization problems to solve and to
people incorporating GlobSol's components into other
systems or providing interfaces to GlobSol.",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
keywords = "constraint propagation; global optimization; GlobSol;
nonconvex optimization",
}
@Book{Moore:2009:IIA,
author = "Ramon E. Moore and R. Baker Kearfott and Michael J.
Cloud",
title = "Introduction to interval analysis",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 223",
year = "2009",
ISBN = "0-89871-669-1",
ISBN-13 = "978-0-89871-669-6",
LCCN = "QA297.75 .M656 2009",
MRclass = "65G40",
MRnumber = "2482682 (2010d:65106)",
MRreviewer = "G. Alefeld",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "http://www.loc.gov/catdir/enhancements/fy0906/2008042348-b.html;
http://www.loc.gov/catdir/enhancements/fy0906/2008042348-d.html;
http://www.loc.gov/catdir/enhancements/fy0906/2008042348-t.html",
ZMnumber = "1168.65002",
abstract = "The use of interval analysis has steadily increased
over the past 40 years. This development was taken into
account when writing the present book. It presents the
basics in real interval arithmetic and covers
elementary methods for verifying and enclosing zeros of
functions, global minimizers, solutions of integral and
differential equations. It deals with integration of
interval functions and shows how interval methods can
be applied in various fields of science. Moreover, an
introduction into the interval toolbox INTLAB of MATLAB
is given in order to understand the many programs which
realize the algorithms of the book. Numerous examples
illustrate the theory and are spread over more than 220
pages.\par
The book starts with a short introduction on the
necessity of enclosures and on bounding roundoff
errors. The interval number system is presented in
Chapter 2 including set theoretic operations as well as
order relations and operations for intervals, interval
vectors, and interval matrices. Some historical
references are added. Chapter 3 discusses the problem
of computing with inexact initial data and therefore
results in first applications of interval arithmetic.
It considers outwardly rounded interval arithmetic and
gives a first glance to INTLAB. Chapter 4 is devoted to
algebraic properties of interval arithmetic, to
symmetric intervals and to inclusion isotonicity.
Interval functions are introduced in Chapter 5
including elementary interval functions and
interval-valued extensions of real functions together
with fundamental properties.\par
The topological side of intervals and of interval
arithmetic is considered in Chapter 6. Equipped with
the Hausdorff metric the set of intervals turns out to
be a complete metric space for which convergence and
continuity can be defined in the usual way. Nested
interval sequences, finite convergence, refinement of
interval extensions, and various centered forms are
additional topics of this chapter which is concluded by
the Skelboe--Moore algorithm. This algorithm is a
prototype of a branch-and-bound algorithm applied in
global optimization. Interval matrices form the subject
of the succeeding Chapter 7, where linear systems with
inexact input data are also discussed. In this
connection the Krawczyk method is mentioned as well as
the interval Gauss--Seidel method and Gaussian
elimination.\par
Nonlinear equations are studied in Chapter 8. Here the
interval Newton method is commented, and cases are
presented which imply the necessity of an extended
interval arithmetic. For systems of nonlinear equations
the Krawczyk method and multivariate interval Newton
methods are applied and safe starting intervals are
defined. Chapter 9 is devoted to the integration of
interval functions, particularly of interval
polynomials since for sufficiently smooth functions $f$
a Taylor expansion is used to construct an enclosure
for $f$. Therefore, automatic differentiation and
automatic generation of Taylor coefficients are also
handled in order to find enclosures for definite
integrals -- also multiple ones -- over $f$. A short
chapter lists some ideas for verifying and enclosing
solutions of integral equations, initial value
problems, and boundary value problems. Some literature
for partial differential equations is added. The final
Chapter 11 gives a first impression of how the tool
`interval analysis' is applied in practice. Problems
are listed which use computer-assisted proofs based on
interval arithmetic. A prototypical algorithm is
discussed for global optimization. Numerous examples
from engineering are mentioned.\par
An appendix covers a variety of topics: Sets and
functions, a formulary for intervals, hints for
selected exercises, Internet resources, and INTLAB
commands and functions. More than 250 references
conclude a wonderful book which is written for all who
are interested in scientific computation, in its
reliability, and in automatic verification of
results.",
acknowledgement = ack-nhfb,
keywords = "automatic differentiation; automatic verification of
results; boundary value problems; branch-and-bound
algorithm; computer-assisted proofs; convergence;
initial value problems; integral equations; interval
analysis; interval arithmetic; interval functions;
interval matrices; interval Newton method; interval
sequences; INTLAB; Krawczyk method; numerical examples;
roundoff errors; scientific computation; Skelboe--Moore
algorithm",
tableofcontents = "Introduction \\
The interval number system \\
First applications of interval arithmetic \\
Further properties of interval arithmetic \\
Introduction to interval function \\
Interval sequences \\
Interval matrices \\
Interval Newton methods \\
Integration of interval functions \\
Integral and differential equations \\
Applications",
}
@Book{Ackleh:2010:CMN,
author = "Azmy S. Ackleh and Edward James Allen and Ralph Baker
Kearfott and Padmanabhan Seshaiyer",
title = "Classical and modern numerical analysis",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "xx + 608",
year = "2010",
ISBN = "1-4200-9157-3",
ISBN-13 = "978-1-4200-9157-1",
LCCN = "QA297 .C53 2010",
MRclass = "65-01",
MRnumber = "2555915",
bibdate = "Mon Aug 23 19:25:57 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Theory, methods and practice",
series = "Chapman \& Hall/CRC Numerical Analysis and Scientific
Computing",
ZMnumber = "1181.65004",
acknowledgement = ack-nhfb,
tableofcontents = "1: Mathematical review and computer arithmetic \\
2: Numerical solution of nonlinear equations of one
variable \\
3: Numerical linear algebra \\
4: Approximation theory \\
5: Eigenvalue-eigenvector computation \\
6: Numerical differentiation and integration \\
7: Initial value problems for ordinary differential
equations \\
8: Numerical solution of systems of nonlinear equations
\\
9: Optimization \\
10: Boundary-value problems and integral equations",
}
@Article{Kearfott:2011:EVL,
author = "R. Baker Kearfott",
title = "Erratum: Validated Linear Relaxations and
Preprocessing: Some Experiments",
journal = j-SIAM-J-OPT,
volume = "21",
number = "1",
pages = "415--416",
month = "????",
year = "2011",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/100816080",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
bibdate = "Thu Jun 9 09:17:33 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/21/1;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
note = "See \cite{Kearfott:2005:VLR}.",
URL = "http://epubs.siam.org/siopt/resource/1/sjope8/v21/i1/p415_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
onlinedate = "March 31, 2011",
}
@Article{Kearfott:2011:ICR,
author = "Ralph Baker Kearfott",
title = "Interval computations, rigour and non-rigour in
deterministic continuous global optimization",
journal = j-OPTIM-METHODS-SOFTW,
volume = "26",
number = "2",
pages = "259--279",
year = "2011",
DOI = "https://doi.org/10.1080/10556781003636851",
ISSN = "1055-6788",
ISSN-L = "1026-7670",
MRclass = "90C26 (90-04)",
MRnumber = "2773658 (2011k:90114)",
bibdate = "Mon Jan 7 15:20:44 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods and Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
}
@Article{Roy:2011:GOS,
author = "J. Roy and R. B. Kearfott",
title = "Global Optimization and Singular Nonlinear Programs:
New Techniques",
journal = j-RELIABLE-COMPUTING,
volume = "15",
number = "3",
pages = "242--250",
year = "2011",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "90C26 (49M37 65G20 65K05)",
MRnumber = "2819088 (2012f:90128)",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kearfott:2013:GFC,
author = "Ralph Baker Kearfott and Jessie Castille and Gaurav
Tyagi",
title = "A general framework for convexity analysis in
deterministic global optimization",
journal = j-J-GLOBAL-OPT,
volume = "56",
number = "3",
pages = "765--785",
year = "2013",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-012-9905-4",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
ISSN-L = "0925-5001",
MRclass = "90C26",
MRnumber = "3070130",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1007/s10898-012-9905-4",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
}
@Article{Kearfott:2013:SRD,
author = "Ralph Baker Kearfott and Sowmya Muniswamy and Yi Wang
and Xinyu Li and Qian Wang",
title = "On smooth reformulations and direct non-smooth
computations for minimax problems",
journal = j-J-GLOBAL-OPT,
volume = "57",
number = "4",
pages = "1091--1111",
year = "2013",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-012-0014-1",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
ISSN-L = "0925-5001",
MRclass = "49J35 (49M15 90C26 90C47)",
MRnumber = "3121784",
MRreviewer = "Jiawei\ Chen",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1007/s10898-012-0014-1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
}
@Article{Kearfott:2014:ANA,
author = "Ralph Baker Kearfott and Jessie M. Castille and Gaurav
Tyagi",
title = "Assessment of a non-adaptive deterministic global
optimization algorithm for problems with
low-dimensional non-convex subspaces",
journal = j-OPTIM-METHODS-SOFTW,
volume = "29",
number = "2",
pages = "430--441",
year = "2014",
DOI = "https://doi.org/10.1080/10556788.2013.780058",
ISSN = "1026-7670 (print), 1055-6788 (electronic)",
ISSN-L = "1026-7670",
ISSN-L = "1026-7670",
MRclass = "90C26 (65K05)",
MRnumber = "3175495",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1080/10556788.2013.780058",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
}
@Article{Kearfott:2014:RUB,
author = "Ralph Baker Kearfott",
title = "On rigorous upper bounds to a global optimum",
journal = j-J-GLOBAL-OPT,
volume = "59",
number = "2-3",
pages = "459--476",
year = "2014",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-014-0173-3",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
ISSN-L = "0925-5001",
MRclass = "90C26",
MRnumber = "3216688",
MRreviewer = "Sirma\ Zeynep\ Alparslan-G{\"{o}}k",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1007/s10898-014-0173-3",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
}
@Article{Kearfott:2015:SOE,
author = "Ralph Baker Kearfott",
title = "Some observations on exclusion regions in branch and
bound algorithms",
journal = j-J-GLOBAL-OPT,
volume = "62",
number = "2",
pages = "229--241",
year = "2015",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-014-0248-1",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
ISSN-L = "0925-5001",
MRclass = "90C56 (90C26)",
MRnumber = "3346728",
MRreviewer = "Warren\ L.\ Hare",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1007/s10898-014-0248-1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
}
@InCollection{Hofschuster:2016:BPW,
author = "Werner Hofschuster and Evgenija D. Popova and Ralph
Baker Kearfott",
booktitle = "Scientific computing, computer arithmetic, and
validated numerics",
title = "Bibliography of {Prof. Walter Kr{\"a}mer}",
volume = "9553",
publisher = pub-SV-CHAM,
address = pub-SV-CHAM:adr,
pages = "281--290",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-31769-4",
ISBN = "97-83319-317-6-9-4; 97-83319-317-6-8-7",
ISBN-13 = "978-3-319-31769-4; 978-3-319-31768-7",
MRclass = "01A70 (65-03 65G30)",
MRnumber = "3516781",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Lecture Notes in Comput. Sci.",
URL = "https://doi.org/10.1007/978-3-319-31769-4",
acknowledgement = ack-nhfb,
}
@Article{Kearfott:2016:PSI,
author = "R. Baker Kearfott",
title = "Preface [{Special} issue in honor of {Ray Moore},
1929--2015]",
journal = j-RELIABLE-COMPUTING,
volume = "23",
pages = "1",
year = "2016",
CODEN = "RCOMF8",
ISSN = "1573-1340",
ISSN-L = "1385-3139",
MRclass = "65-06 (65G30)",
MRnumber = "3538347",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Guilbeau:2017:RCM,
author = "Jared T. Guilbeau and Md. Istiaq Hossain and Sam D.
Karhbet and Ralph Baker Kearfott and Temitope S. Sanusi
and Lihong Zhao",
title = "A review of computation of mathematically rigorous
bounds on optima of linear programs",
journal = j-J-GLOBAL-OPT,
volume = "68",
number = "3",
pages = "677--683",
year = "2017",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-016-0489-2",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
ISSN-L = "0925-5001",
MRclass = "90C05 (90-04)",
MRnumber = "3661094",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1007/s10898-016-0489-2",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
}
@Article{Karhbet:2017:RBF,
author = "Sam Karhbet and Ralph Baker Kearfott",
title = "Range bounds of functions over simplices, for branch
and bound algorithms",
journal = j-RELIABLE-COMPUTING,
volume = "25",
pages = "53--73",
year = "2017",
CODEN = "RCOMF8",
ISSN = "1573-1340",
ISSN-L = "1385-3139",
MRclass = "65K10 (90C30 90C56)",
MRnumber = "3678567",
MRreviewer = "Savin\ Trean\c{t}\u{a}",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing",
journal-URL = "http://link.springer.com/journal/11155",
}
@InCollection{Kearfott:2021:MRG,
author = "Ralph Baker Kearfott",
booktitle = "Black box optimization, machine learning, and no-free
lunch theorems",
title = "Mathematically rigorous global optimization and fuzzy
optimization",
volume = "170",
publisher = pub-SV-CHAM,
address = pub-SV-CHAM:adr,
pages = "169--194",
year = "2021",
DOI = "https://doi.org/10.1007/978-3-030-66515-9\_7",
ISBN = "97-83030-665-1-5-9; 97-83030-665-1-4-2",
ISBN-13 = "978-3-030-66515-9; 978-3-030-66514-2",
MRclass = "90C56 (03E72 90C26 90C70)",
MRnumber = "4287651",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Springer Optim. Appl.",
URL = "https://doi.org/10.1007/978-3-030-66515-9_7",
acknowledgement = ack-nhfb,
}
@Article{Lizarralde-Bejarano:2022:MUE,
author = "Diana Paola Lizarralde-Bejarano and Hayriye Gulbudak
and Ralph Baker Kearfott and Mar{\'{}\i}a Eugenia
Puerta-Yepes",
title = "Modeling the uncertainty in epidemiological models
through interval analysis considering actual data from
two municipalities in {Colombia} affected by dengue",
journal = j-APPL-MATH-MODEL,
volume = "111",
pages = "739--752",
year = "2022",
CODEN = "AMMODL",
DOI = "https://doi.org/10.1016/j.apm.2022.07.006",
ISSN = "0307-904X (print), 1872-8480 (electronic)",
ISSN-L = "0307-904X",
ISSN-L = "0307-904X",
MRclass = "92D30 (62P10)",
MRnumber = "4458165",
bibdate = "Wed Oct 18 11:47:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
URL = "https://doi.org/10.1016/j.apm.2022.07.006",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematical Modelling. Simulation and
Computation for Engineering and Environmental Systems",
journal-URL = "http://www.sciencedirect.com/journal/applied-mathematical-modelling",
}
@Article{Huang:1998:IEP,
author = "Zhenyu Huang",
title = "An Interval Entropy Penalty Method for Nonlinear
Global Optimization",
journal = j-RELIABLE-COMPUTING,
volume = "4",
number = "1",
pages = "15--25",
month = feb,
year = "1998",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1009994414947",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 16:00:43 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=4&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
note = "See errata and comments \cite{Kearfott:2005:EOI}.",
URL = "http://link.springer.com/article/10.1023/A%3A1009994414947/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=4&issue=1&spage=15;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=4&issue=1&spage=15-25",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Book{Kreinovich:1998:CCF,
author = "Vladik Kreinovich and Anatoly Lakeyev and Ji{\v{r}}i
Rohn and Patrick Kahl",
title = "Computational Complexity and Feasibility of Data
Processing and Interval Computations",
volume = "10",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xii + 459",
year = "1998",
ISBN = "0-7923-4865-6 (hardcover)",
ISBN-13 = "978-0-7923-4865-8 (hardcover)",
LCCN = "QA267.7 .C68 1998",
bibdate = "Mon Feb 6 12:14:14 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied optimization",
URL = "http://www.loc.gov/catdir/enhancements/fy0814/97043085-d.html;
http://www.loc.gov/catdir/enhancements/fy0814/97043085-t.html",
acknowledgement = ack-nhfb # " and " # ack-vk,
subject = "Computational complexity; Numerical calculations; Data
processing; Interval analysis (Mathematics)",
}
@Proceedings{Cohen:1982:IFE,
editor = "B. A. Cohen",
booktitle = "{IEEE 1981 frontiers of engineering in health care:
September 19--21, 1981, Shamrock Hilton Hotel, Houston,
Texas: the 3rd annual conference of the Engineering in
Medicine and Biology Society of the Institute of
Electrical and Electronics Engineers}",
title = "{IEEE 1981 frontiers of engineering in health care:
September 19--21, 1981, Shamrock Hilton Hotel, Houston,
Texas: the 3rd annual conference of the Engineering in
Medicine and Biology Society of the Institute of
Electrical and Electronics Engineers}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "455",
year = "1982",
LCCN = "R856.A2 I344 1981a",
bibdate = "Tue May 23 16:28:41 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
xxISBN = "none",
}
@Proceedings{Pereyra:1982:NM,
editor = "V. Pereyra and A. Reinoza",
booktitle = "Numerical Methods: Proceedings of the international
workshop held at {Caracas, June 14--18, 1982}",
title = "Numerical Methods: Proceedings of the international
workshop held at {Caracas, June 14--18, 1982}",
volume = "1005",
publisher = pub-SV,
address = pub-SV:adr,
pages = "296",
year = "1982",
DOI = "https://doi.org/10.1007/978-0-387-12334-9",
ISBN = "0-387-12334-2 (New York), 3-540-12334-2 (Berlin)",
ISBN-13 = "978-0-387-12334-9 (New York), 978-3-540-12334-7
(Berlin)",
LCCN = "QA3 .L35 v.1005, QA 297 N86 1982",
bibdate = "Tue May 23 16:33:47 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Lecture Notes in Mathematics",
}
@Proceedings{Potvin:1982:FEH,
editor = "Alfred R. Potvin and Janet H. Potvin",
booktitle = "{Frontiers of engineering in health care, 1982:
proceedings, Fourth Annual Conference, IEEE Engineering
in Medicine and Biology Society, Marriott Hotel,
Philadelphia, PA, 20--21 September 1982}",
title = "{Frontiers of engineering in health care, 1982:
proceedings, Fourth Annual Conference, IEEE Engineering
in Medicine and Biology Society, Marriott Hotel,
Philadelphia, PA, 20--21 September 1982}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "633",
year = "1982",
LCCN = "W3 IE34 1982",
bibdate = "Wed May 24 15:12:40 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Kuepper:1984:NMB,
editor = "T. K{\"u}pper and H. D. Mittelmann and H. Weber",
booktitle = "Numerical Methods for Bifurcation Problems:
Proceedings of the Conference at the {University of
Dortmund, August 22--26, 1983}",
title = "Numerical Methods for Bifurcation Problems:
Proceedings of the Conference at the {University of
Dortmund, August 22--26, 1983}",
number = "70",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
year = "1984",
ISBN = "3-7643-1627-6",
ISBN-13 = "978-3-7643-1627-3",
LCCN = "QA297 .N864 1984",
bibdate = "Tue May 23 16:30:27 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "International Series of Numerical Mathematics (ISNM)",
}
@Proceedings{Vichnevetsky:1988:PTI3,
editor = "R. Vichnevetsky and P. Borne and J. Vignes",
booktitle = "Proceedings of the Twelfth {IMACS} World Congress on
Scientific Computation 3 ({July 18--22 1988, Paris,
France})",
title = "Proceedings of the Twelfth {IMACS} World Congress on
Scientific Computation 3 ({July 18--22 1988, Paris,
France})",
publisher = "IMACS",
address = "Villeneuve d'Asq, France",
pages = "various",
year = "1988",
ISBN = "2-9502908-0-9",
ISBN-13 = "978-2-9502908-0-9",
LCCN = "QA 76.9 C65 I43 1988",
bibdate = "Tue May 23 16:55:41 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Five volumes.",
}
@Proceedings{Vichnevetsky:1988:PTI4,
editor = "R. Vichnevetsky and P. Borne and J. Vignes",
booktitle = "Proceedings of the Twelfth {IMACS} World Congress on
Scientific Computation 4",
title = "Proceedings of the Twelfth {IMACS} World Congress on
Scientific Computation 4",
publisher = "IMACS",
address = "Villeneuve d'Asq, France",
pages = "various",
year = "1988",
ISBN = "2-9502908-0-9",
ISBN-13 = "978-2-9502908-0-9",
LCCN = "QA 76.9 C65 I43 1988",
bibdate = "Tue May 23 16:55:44 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Five volumes.",
}
@Proceedings{Bowers:1989:CC,
editor = "K. Bowers and J. Lund",
booktitle = "Computation and Control: Proceedings of the {Bozeman}
conference, {Bozeman, Montana, August 1--11, 1988}",
title = "Computation and Control: Proceedings of the {Bozeman}
conference, {Bozeman, Montana, August 1--11, 1988}",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "410",
year = "1989",
ISBN = "0-8176-3438-X",
ISBN-13 = "978-0-8176-3438-4",
LCCN = "TA329 .C6451 1989",
bibdate = "Tue May 23 16:28:46 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "Progress in Systems and Control Theory",
}
@Proceedings{Eisenfeld:1989:BSM,
editor = "Jerome Eisenfeld and Daniel S. Levine",
booktitle = "Biomedical Systems Modelling and Simulation",
title = "Biomedical Systems Modelling and Simulation",
number = "5",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "207",
year = "1989",
ISBN = "3-905135-64-7",
ISBN-13 = "978-3-905135-64-0",
LCCN = "QH323.5 .B56 1989",
bibdate = "Wed May 24 14:36:12 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = "IMACS transactions on scientific computing",
}
@Proceedings{Sharda:1989:IRC,
editor = "R. Sharda and B. L. Golden and E. Wasil and O. Balci
and G. W. Stewart",
booktitle = "Impacts of Recent Computer Advances on Operations
Research",
title = "Impacts of Recent Computer Advances on Operations
Research",
volume = "9",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xii + 585",
year = "1989",
ISBN = "0-444-01492-6",
ISBN-13 = "978-0-444-01492-4",
LCCN = "T57.6 .I4831 1989",
bibdate = "Wed May 28 17:52:37 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
z3950.loc.gov:7090/Voyager",
series = "Publications in Operations Research",
URL = "http://www.zentralblatt-math.org/zmath/en/search/?an=0727.90047",
ZMnumber = "0727.90047",
acknowledgement = ack-nhfb,
subject = "Operations research; Data processing",
tableofcontents = "\\
I. Plenary papers \\
\\
G. B. Dantzig / Decomposition techniques for
large-scale electric power systems planning under
uncertainty / 3--22 \\
\\
II. Parallel algorithms for mathematical programming
\\
\\
R. S. Barr, M. G. Christiansen / A parallel auction
algorithm: A case study in the use of parallel
object-oriented programming, 23--32 \\
J. O. Berkey, P. Y. Wang / A comparative study of some
parallel bin packing algorithms / 33--43 \\
T. E. Gerasch, P. Y. Wang, S. T. Weidman / SIMD
knapsack approximation algorithms / 44-- 56 \\
A. R. Joshi, D.-S. Chen / A vectorized dual algorithm
for generalized network problem / 57--70 \\
H. S. Mahmassani, K. C. Mouskos / Vectorization of
transportation network equilibrium assignment codes /
71--81 \\
G. L. Schultz, R. R. Meyer / A flexible parallel
algorithm for block-constrained optimization problems /
82--91 \\
R. Hunter Mladineo / Supercomputers and global
optimization / 92--105 \\
J. M. Mulvey, H. Vladimirou / Evaluation of a parallel
hedging algorithm for stochastic network programming /
106--119 \\
D. M. Nicol / Parallel solution of dynamic programming
equation using optimistic evaluation / 120--130 \\
P. M. Pardalos, G. P. Rodgers / Parallel branch and
bound algorithms for unconstrained quadratic zero-one
programming / 131--143 \\
G. Plateau, C. Roucairol / A supercomputer algorithm
for the 0--1 multiknapsack problem / 144--157 \\
M. J. Saltzman, R. Subramanian, R. E. Marsten /
Implementing an interior point LP algorithm on a
supercomputer / 158--168 \\
C. Phillips, S. A. Zenios / Experiences with large
scale network optimization on the connection machine /
169--182 \\
\\
III. Graphics in optimization \\
\\
I. Lustig / Application of interactive computer
graphics to linear programming / 183--189 \\
C. L. Monma, D. F. Shallcross / A PC-based interactive
network design system for fiber optic communication
networks / 190--204 \\
\\
IV. Microcomputers in operations research \\
\\
E. Gelman, M. A. Pollatschek / Personal computer
version of nearly triangular Leontief LP solution /
205--216 \\
T. P. Harrison, J. L. Martin / Optimizing exchange
agreements in the refining industry / 217-- 225 \\
J. K. Ho / Nonprocedural implementation of mathematical
programming algorithms / 226--237 \\
R. Terry, D. DeBald, R. Chikkala / Closed queueing
network analysis of indirect labor requirements /
238--247 \\
M. L. Villanueva, N. A. Wittpenn, C. B. Austin, E.
Baker / A microcomputer-based marine geographic
information system with marketing application /
248--262 \\
E. Wasil, B. Golden, R. Sharda / Mathematical
programming software for the microcomputer: Recent
advances, comparisons and trends / 263--272 \\
E. Wasil, A. Assad / Project management software for
the microcomputer: Recent advances and future
directions / 273--288 \\
\\
V. Artificial intelligence and expert systems \\
\\
G. Anandalingam, R. Mathieu, C. L. Pittard, N. Sinha /
Artificial intelligence based approaches for solving
hierarchical optimization problems / 289--301 \\
J. W. Denton, G. R. Madey / Impact of neurocomputing on
operations research / 302--312 \\
H. J. Greenberg / Neural networks for an intelligent
mathematical programming system / 313-- 320 \\
M. R. Hilliard, G. E. Liepins, M. Palmer, G. Rangarajan
/ The computer as a partner in algorithmic design:
Automated discovery of parameters for a multi-objective
scheduling heuristic / 321--331 \\
J.- Y. Potvin, S. F. Smith / Flexible systems for the
design of heuristic algorithms in complex OR domains /
332--346 \\
\\
VI. Vehicle routing and scheduling applications \\
\\
D. Jovanovic, P. T. Harker / SCAN: A decision support
system for railroad scheduling / 347--360 \\
K. E. Nygard, P. Juell, K. Nagesh / An interactive
decision support system for vehicle routing / 361--372
\\
J. R. Schaffer, P. K. Pearl / Vehicle routing and
scheduling for home delivery / 373--384 \\
\\
VII. Simulation \\
\\
O. Balci, R. E. Nance / Simulation model development:
The multidimensionality of the computing technology
pull / 385--395 \\
R. K. Kincaid, K. W. Miller, S. K. Park / Locating P
mobile servers on a congested network: A simulation
analysis / 396--406 \\
R. L. Moose, R. E. Nance / The design and development
of an analyzer for discrete event model specifications
/ 407--421 \\
R. J. Paul / Visual simulation: Seeing is believing?
422--432 \\
M. B. Silberholz, B. L. Golden, E. K. Baker /
Simulating a marine container terminal on the Macintosh
II / 433 \\
\\
VIII. Model development and analysis systems \\
\\
G. H. Bradley / Mathematical programming modeling
project - overview / 447--462 \\
R. G. Brown, J. W. Chinneck, G. M. Karam / Optimization
with constraint programming systems / 463--473 \\
M. Grauer, S. Albers, M. Frommberger / Concept and
first experiences with an object-oriented interface for
mathematical programming / 474--483 \\
G. Mitra / Tools for modelling support and construction
of optimization applications / 484--496 \\
A. D. Waren, M. Pechura, L. S. Lasdon / The GRG2 model
builder / 497--506 \\
S. Zenios, S. S. Nielsen, M. Pinar / On the use of
advance architecture computers via high-level modelling
languages / 507 \\
\\
IX. Telecommunications \\
\\
A. J. Perticone, J. P. Jarvis, D. R. Shier / Evaluation
and design of voice telecommunications network /
521--532 \\
\\
X. Numerical analysis \\
\\
R. Baker Kearfott / Interval arithmetic methods for
nonlinear systems and nonlinear optimization: An
outline and status / 533--542 \\
A. P. Morgan / Polynomial continuation / 543--554 \\
L. T. Watson / Modern homotopy methods in optimization
/ 555--566",
}
@Proceedings{Allgower:1990:CSN,
editor = "E. L. Allgower and K. Georg",
booktitle = "Computational Solution of Nonlinear Systems of
Equations ({Fort Collins, CO}, 1988)",
title = "Computational Solution of Nonlinear Systems of
Equations ({Fort Collins, CO}, 1988)",
volume = "26",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xix + 762",
year = "1990",
ISBN = "0-8218-1131-2",
ISBN-13 = "978-0-8218-1131-3",
LCCN = "QA372 .C6374 1990",
bibdate = "Tue May 23 16:22:53 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
series = "Lectures in Applied Mathematics",
mynote = "Proc. of 1988 SIAM-AMS summer seminar",
}
@Proceedings{Law:1990:AOC,
editor = "A. G. Law and C. L. Wang",
booktitle = "Approximation, Optimization, and Computing: Theory and
Applications",
title = "Approximation, Optimization, and Computing: Theory and
Applications",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xv + 442",
year = "1990",
ISBN = "0-444-88693-1",
ISBN-13 = "978-0-444-88693-4",
LCCN = "QA221 .A64 1990",
bibdate = "Tue May 23 16:55:48 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Proceedings{Dongarra:1992:PFS,
editor = "J. Dongarra and K. Kennedy and P. Messina and D. C.
Sorensen and R. G. Voigt",
booktitle = "Proceedings of the Fifth {SIAM} Conference on Parallel
Processing for Scientific Computing",
title = "Proceedings of the Fifth {SIAM} Conference on Parallel
Processing for Scientific Computing",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xvii + 648",
year = "1992",
ISBN = "0-89871-303-X",
ISBN-13 = "978-0-89871-303-9",
LCCN = "QA76.58 .P76 1992",
bibdate = "Tue May 23 16:28:45 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
}
@Proceedings{Albrecht:1993:VNT,
editor = "R. Albrecht and G. Alefeld and H. J. Stetter",
booktitle = "Validation numerics: theory and applications",
title = "Validation numerics: theory and applications",
volume = "9",
publisher = pub-SPRINGER-WIEN,
address = pub-SPRINGER-WIEN:adr,
pages = "291",
year = "1993",
CODEN = "COSPDM",
ISBN = "0-387-82451-0 (New York), 3-211-82451-0 (Vienna)",
ISBN-13 = "978-0-387-82451-2 (New York), 978-3-211-82451-1
(Vienna)",
ISSN = "0344-8029",
LCCN = "QA297 .V27 1993",
bibdate = "Wed Oct 13 18:45:11 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib",
note = "Dedicated to Ulrich Kulisch on the occasion of his
60th birthday.",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
}
@Proceedings{Corliss:1993:AIC,
editor = "G. F. Corliss and R. B. Kearfott",
booktitle = "Abstracts for an {International Conference on
Numerical Analysis with Automatic Result Verification:
Mathematics, Application and Software, February
25--March 1, 1993, Lafayette, LA, 1993}",
title = "Abstracts for an {International Conference on
Numerical Analysis with Automatic Result Verification:
Mathematics, Application and Software, February
25--March 1, 1993, Lafayette, LA, 1993}",
volume = "3(3--4)",
publisher = "????",
address = "????",
pages = "????",
year = "1993",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0135-4868",
LCCN = "????",
bibdate = "Tue Oct 22 13:32:36 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
series = j-INTERVAL-COMP,
acknowledgement = ack-nhfb,
xxtitle = "Numerical analysis with automatic result verification:
International conference: Selected papers",
}
@Proceedings{Kearfott:1993:PICa,
editor = "R. Baker Kearfott",
title = "{Proceedings of the international conference on
numerical analysis with automatic result verification,
Lafayette, LA, USA, February 25--March 1, 1993}",
journal = j-INTERVAL-COMP,
volume = "3",
pages = "208",
year = "1993",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:08:37 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Published in {\em Interval Computing}, Number 3.",
ZMnumber = "0828.00044",
abstract = "{The articles of this volume will be reviewed
individually within the journal ``Interval Comput.
1993, No. 3 (1993)".}",
acknowledgement = ack-nhfb,
classmath = "{00B25 (Proceedings of conferences of miscellaneous
specific interest) 65-06 (Proceedings of conferences
(numerical analysis)) }",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "Automatic result verification; Conference; Lafayette,
LA (USA); Numerical analysis; Proceedings",
language = "English; Russian",
}
@Proceedings{Kearfott:1993:PICb,
editor = "R. Baker Kearfott",
booktitle = "{Proceedings of the international conference on
numerical analysis with automatic result verification,
Lafayette, LA, USA, February 25-- March 1, 1993}",
title = "{Proceedings of the international conference on
numerical analysis with automatic result verification,
Lafayette, LA, USA, February 25--March 1, 1993}",
journal = j-INTERVAL-COMP,
volume = "4",
pages = "211",
year = "1993",
ISSN = "0135-4868",
bibdate = "Tue Aug 24 09:08:37 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
note = "Published in {\em Interval Computing}, Number 4.",
ZMnumber = "0828.00045",
acknowledgement = ack-nhfb,
classmath = "00B25 (Proceedings of conferences of miscellaneous
specific interest) 65-06 (Proceedings of conferences
(numerical analysis))",
fjournal = "Interval Computations = Interval'nye vychisleniia",
keywords = "Automatic result verification; Conference; Lafayette,
LA (USA); Numerical analysis; Proceedings",
language = "English; Russian",
}
@Proceedings{Kearfott:1994:NAA,
editor = "R. B. Kearfott and G. F. Corliss",
booktitle = "{Numerical analysis with automatic result
verification: International conference --- February
1993, Lafayette, LA}",
title = "{Numerical analysis with automatic result
verification: International conference --- February
1993, Lafayette, LA}",
number = "3 (or 4??)",
publisher = "Institute for new technologies",
address = "????",
pages = "????",
year = "1994",
ISSN = "0135-4868",
bibdate = "Mon Oct 20 07:16:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
series = "INTERVAL COMPUTATIONS 1993",
acknowledgement = ack-nhfb,
}
@Proceedings{Kearfott:1996:AIC,
editor = "R. Baker Kearfott and Vladik Kreinovich",
booktitle = "Applications of interval computations: Papers
presented at an international workshop in {El Paso,
Texas, February 23--25, 1995}",
title = "Applications of interval computations: Papers
presented at an international workshop in {El Paso,
Texas, February 23--25, 1995}",
volume = "3",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvii + 425",
year = "1996",
ISBN = "0-7923-3847-2",
ISBN-13 = "978-0-7923-3847-5",
LCCN = "QA297.75.A66 1996",
MRclass = "65-01 (65G10)",
MRnumber = "1386897 (96m:65001)",
bibdate = "Mon Oct 20 07:16:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "``Applications of Interval Computations'' contains
primarily survey articles of actual industrial
applications of numerical analysis with automatic
result verification and of interval representation of
data.
Underlying topics include: \begin{itemize} \item branch
and bound algorithms for global optimization, \item
constraint propagation, \item solution sets of linear
systems, \item hardware and software systems for
interval computations, and \item fuzzy logic.
\end{itemize}
Actual applications described in the book include:
\begin{itemize} \item economic input-output models,
\item quality control in manufacturing design, \item a
computer-assisted proof in quantum mechanics, \item
medical expert systems, \item and others.
\end{itemize}
A realistic view of interval computations is taken: the
articles indicate when and how overestimation and other
challenges can be overcome.
An introductory chapter explains the content of the
papers in terminology accessible to mathematically
literate graduate students. The style of the
individual, refereed contributions has been made
uniform and understandable, and there is an extensive
book-wide index.
Audience: Valuable to students and researchers
interested in automatic result verification.
Detailed information, including contents, contributors,
and an order form can be found: \begin{itemize} \item
on Kluwer homepage \path=http://www.wkap.nl=, or \item
on the Interval Computations homepage
\path=http://cs.utep.edu/interval-comp/main.html=, in
the ``Books'' section. \end{itemize} The information on
the Interval Computations homepage is basically a
mirror image of the Kluwer one (the only difference is
that the fonts are fancier).",
series = "Applied Optimization",
acknowledgement = ack-nhfb # " and " # ack-dgh,
}
@Proceedings{Alt:2004:NSR,
editor = "Ren{\'e} Alt and Andreas Frommer and R. Baker Kearfott
and Wolfram Luther",
booktitle = "{Numerical Software with Result Verification:
International Dagstuhl Seminar, Dagstuhl Castle,
Germany, January 19--24, 2003. Revised Papers}",
title = "{Numerical Software with Result Verification:
International Dagstuhl Seminar, Dagstuhl Castle,
Germany, January 19--24, 2003. Revised Papers}",
volume = "2991",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 315",
year = "2004",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-540-21260-7;
https://doi.org/10.1007/b96498",
ISBN = "3-540-21260-4 (paperback), 3-540-24738-6 (e-book)",
ISBN-13 = "978-3-540-21260-7 (paperback), 978-3-540-24738-8
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA297 .N867 2004",
bibdate = "Tue Aug 24 08:43:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2991.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2991;
http://www.springeronline.com/3-540-21260-4",
ZMnumber = "1046.65001",
acknowledgement = ack-nhfb,
classmath = "65-06 (Proceedings of conferences (numerical
analysis)) 68-06 (Proceedings of conferences (computer
science)) 00B25 (Proceedings of conferences of
miscellaneous specific interest) 65Y99 (Computer
aspects of numerical algorithms)",
}
@Book{Hu:2008:KPI,
editor = "Chenyi Hu and R. Baker Kearfott and Andre de Korvin",
booktitle = "Knowledge processing with interval and soft
computing",
title = "Knowledge processing with interval and soft
computing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 233",
year = "2008",
ISBN = "1-84800-325-0 (hardcover), 1-84800-326-9 (ebook)",
ISBN-13 = "978-1-84800-325-5 (hardcover), 978-1-84800-326-2
(ebook)",
LCCN = "QA76.9.D343.K669 2008",
bibdate = "Wed Nov 19 09:35:36 MST 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
z3950.loc.gov:7090/Voyager",
series = "Advanced information and knowledge processing",
acknowledgement = ack-nhfb,
tableofcontents = "1. Fundamentals of Interval Computing / Ralph Baker
Kearfott and Chenyi Hu \\
2. Soft Computing Essentials / Andre de Korvin, Hong
Lin and Plamen Simeonov \\
3. Relations Between Interval Computing and Soft
Computing / Vladik Kreinovich \\
4. Interval Matrices in Knowledge Discovery / Chenyi Hu
and R. Baker Kearfott \\
5. Interval Function Approximation and Applications /
Chenyi Hu, Ling T. He and Shanying Xu \\
6. Interval Rule Matrices for Decision Making / Chenyi
Hu \\
7. Interval Matrix Games / W. Dwayne Collins and Chenyi
Hu \\
8. Interval-Weighted Graphs and Flow Networks / Chenyi
Hu and Ping Hu \\
9. Arithmetic on Bounded Families of Distributions: A
DEnv Algorithm Tutorial / Daniel Berleant, Gary
Anderson and Chaim Goodman-Strauss \\
10. IntBox: An Object-Oriented Interval Computing
Software Toolbox in C++ / Michael Nooner and Chenyi Hu
\\
Index",
}
