%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "R. Baker Kearfott", %%% version = "2.15", %%% date = "19 February 2013", %%% time = "16:27:21 MST", %%% filename = "kearfott-r-baker.bib", %%% address = "University of Southwestern Louisiana %%% Department of Mathematics %%% Lafayette, LA 70504-1010 %%% USA", %%% telephone = "+1 318 482 5270", %%% FAX = "+1 318 482 5346", %%% URL = "ftp://interval.usl.edu/pub/interval_math/www/kearfott.html", %%% checksum = "41852 4050 18237 191222", %%% email = "rbk5287 at interval.usl.edu (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "nonlinear equations, optimization, interval arithmetic", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications of %%% R. Baker Kearfott. The companion LaTeX file %%% kearfott-r-baker.ltx can be used to typeset %%% this bibliography. %%% %%% At version 2.15, the year coverage looked %%% like this: %%% %%% 1972 ( 1) 1986 ( 0) 2000 ( 2) %%% 1973 ( 0) 1987 ( 4) 2001 ( 1) %%% 1974 ( 0) 1988 ( 8) 2002 ( 4) %%% 1975 ( 0) 1989 ( 9) 2003 ( 7) %%% 1976 ( 0) 1990 ( 9) 2004 ( 3) %%% 1977 ( 1) 1991 ( 4) 2005 ( 4) %%% 1978 ( 1) 1992 ( 11) 2006 ( 1) %%% 1979 ( 2) 1993 ( 13) 2007 ( 1) %%% 1980 ( 1) 1994 ( 17) 2008 ( 5) %%% 1981 ( 1) 1995 ( 7) 2009 ( 3) %%% 1982 ( 4) 1996 ( 11) 2010 ( 1) %%% 1983 ( 3) 1997 ( 2) 2011 ( 3) %%% 1984 ( 2) 1998 ( 6) %%% 1985 ( 0) 1999 ( 2) %%% %%% Article: 74 %%% Book: 5 %%% InCollection: 14 %%% InProceedings: 16 %%% MastersThesis: 2 %%% Misc: 18 %%% PhdThesis: 5 %%% Proceedings: 19 %%% TechReport: 1 %%% %%% Total entries: 154 %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access on ftp.math.utah.edu in the %%% directory tree /pub/bibnet/authors. It is %%% mirrored to netlib.bell-labs.com in the directory %%% tree /netlib/bibnet/authors, from which it is %%% available via anonymous ftp and the Netlib %%% service. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" } %%% ==================================================================== %%% Journal abbreviations: @String{j-ANN-OPER-RESEARCH= "Annals of Operations Research"} @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"} %%% ==================================================================== %%% Publisher abbreviations: @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-NH= "North-Hol{\-}land"} @String{pub-NH: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."} %%% ==================================================================== %%% Series abbreviations: @String{ser-LNCS= "Lecture Notes in Computer Science"} %%% ==================================================================== %%% Bibliography entries: @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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, } @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 (paper), 1088-6842 (electronic)", 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 = "http://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", 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 = "http://dx.doi.org/10.1007/BF01404868", ISSN = "0029-599X (print), 0945-3245 (electronic)", 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 = "http://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", 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, pages = "627--633", year = "1979", ISBN = "0-12-434180-2", ISBN-13 = "978-0-12-434180-7", LCCN = "QA300 .I48 1978", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", ZMnumber = "0454.65040", bookpages = "xx + 726", 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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, } @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 = "http://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 = "http://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 = "140--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 = "Tue Aug 24 09:44:22 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.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", } @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 = "http://dx.doi.org/10.2307/2007693", ISSN = "0025-5718 (paper), 1088-6842 (electronic)", MRclass = "65D30 (41A99)", MRnumber = "85g:65029", MRreviewer = "B. Boyanov", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; JSTOR database", ZMnumber = "0523.65018", acknowledgement = ack-nhfb, } @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 = "http://dx.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 = "http://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", 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 = "http://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 = "http://dx.doi.org/10.2307/2008257", ISSN = "0025-5718 (paper), 1088-6842 (electronic)", 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 = "http://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", 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 = "http://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 = "http://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)", MRclass = "65H10", MRnumber = "88m:65081", bibdate = "Sat Nov 19 13:08:33 1994", bibsource = "http://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, 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 = "http://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 = "http://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)", MRclass = "399 (1989). 65H10", MRnumber = "1 062 485, 88m:65081", bibdate = "Sat Nov 19 13:04:08 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", note = "See \cite{Kearfott:1987:STG}.", ZMnumber = "0666.65040", acknowledgement = ack-nhfb, 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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)", bibdate = "Sun Sep 04 23:09:48 1994", bibsource = "http://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, 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 = "http://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)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://dx.doi.org/10.1137/0727047", ISSN = "0036-1429 (print), 1095-7170 (electronic)", MRclass = "65H10 (65G10)", MRnumber = "91d:65072", MRreviewer = "G. Alefeld", bibdate = "Mon Jan 20 15:27:00 MST 1997", bibsource = "http://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 $A \in IA$ and $R \in IR$, 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 $IR$ of vectors. Bounds on the vector $Y$ are sought as $A$ ranges over $IA$ and $R$ ranges over $IR$. \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) }", 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; http://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", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://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 = "http://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 = "http://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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fortran3.bib; http://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 = "http://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 = "http://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)) }", 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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fortran3.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://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)", bibdate = "Sat May 20 15:54:18 1995", bibsource = "http://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, 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://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 = "http://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)", MRclass = "65G10 (65H10)", MRnumber = "94m:65076", bibdate = "Mon Jan 20 15:27:00 MST 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, } @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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @Article{Ning:1994:CME, author = "S. Ning and R. B. Kearfott", title = "A Comparison of Methods for Estimating the Solution Hull of Systems of Linear Interval Equations", journal = j-SIAM-J-NUMER-ANAL, volume = "??", number = "??", pages = "??--??", month = "????", year = "1994", CODEN = "SJNAAM", ISSN = "0036-1429", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://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)) }", 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 = "http://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))", 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", 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)", bibdate = "Sat May 20 15:54:41 1995", bibsource = "http://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, 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)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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/article/10.1007/BF02390516; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=1&spage=3 http://link.springer.com/accesspage/article/10.1007/BF02390516; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=1&spage=3-4", acknowledgement = ack-nhfb, fjournal = "Reliable Computing = Nadezhnye vychisleniia", journal-URL = "http://www.springerlink.com/content/1385-3139", } @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 = "http://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 = "http://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)", bibsource = "http://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, 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 = "http://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 = "http://dx.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; http://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", 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", 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 = "http://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 = "http://dx.doi.org/10.1137/S1064827594266131", ISSN = "1064-8275 (print), 1095-7197 (electronic)", MRclass = "65G10 (65H20); 65G10 (65Hxx)", MRnumber = "1433796 (97m:65094)", MRreviewer = "J. Michel Muller", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", ZMnumber = "0871.65042", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", } @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 = "http://dx.doi.org/10.1137/S0036142994270995", ISSN = "0036-1429 (print), 1095-7170 (electronic)", MRclass = "65G10 (65F05)", MRnumber = "1461785 (98m:65081)", MRreviewer = "H. Ratschek", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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, 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 = "http://dx.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 = "http://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", } @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)", bibdate = "Thu Apr 9 08:47:36 MDT 1998", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, } @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 = "http://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 = "http://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 = "http://dx.doi.org/10.1137/S0036142999361074", ISSN = "0036-1429 (print), 1095-7170 (electronic)", 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 = "http://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", } @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 = "http://dx.doi.org/10.1145/358407.358418", ISSN = "0098-3500 (print), 1557-7295 (electronic)", MRclass = "65G20 (65H10 90C30)", MRnumber = "1809949 (2001i:65058)", MRreviewer = "K. Schittkowski", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, fjournal = "Association for Computing Machinery. Transactions on Mathematical Software", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.doi.org/10.1006/jcom.2001.0634", ISSN = "0885-064X (print), 1090-2708 (electronic)", MRclass = "65H10 (65G20)", MRnumber = "1919451 (2003g:65068)", MRreviewer = "B. Kellogg", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", } @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 = "http://dx.doi.org/10.1090/S0025-5718-02-01427-8", ISSN = "0025-5718 (paper), 1088-6842 (electronic)", MRclass = "65G20 (65H10)", MRnumber = "1954966 (2004a:65056)", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.doi.org/10.1137/S0036142901386057", ISSN = "0036-1429 (print), 1095-7170 (electronic)", MRclass = "65H10", MRnumber = "2034619 (2004i:65045)", MRreviewer = "M. A. Wolfe", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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 $d\ge2$: 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", keywords = "algorithm; interval computations; numerical examples; singularities; topological degree; verified computations; complex nonlinear systems", } @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 = "http://dx.doi.org/10.1007/b94062", bibdate = "Tue Aug 24 08:30:55 2010", bibsource = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib", URL = "http://link.springer.com/article/10.1023%2FA%3A1025127211629", ZMnumber = "1039.65500", acknowledgement = ack-nhfb, classmath = "{65-06 (Proceedings of conferences (numerical analysis)) 00B25 (Proceedings of conferences of miscellaneous specific interest) }", journal-URL = "http://www.springerlink.com/content/1385-3139", } @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 = "http://dx.doi.org/10.1007/b96498", bibdate = "Tue Aug 24 08:39:43 2010", bibsource = "http://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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", 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 = "http://dx.doi.org/10.1137/030602186", ISSN = "1052-6234 (print), 1095-7189 (electronic)", MRclass = "90C30 (65G20 65K10 68Q25 90C26)", MRnumber = "2197988 (2006m:90160)", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", 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 = "http://dx.doi.org/10.1007/s10898-004-2120-1", ISSN = "0925-5001", MRclass = "90C25 (68Q17 90C26 90C60)", MRnumber = "2190763 (2006g:90084)", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", keywords = "Computational complexity; Global optimization; Non-convexity", mrrclass = "90C25 (68Q17 90C26 90C60)", } @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 = "http://dx.doi.org/10.1080/10556780500130525", ISSN = "1055-6788", MRclass = "90C30 (65G40)", MRnumber = "2238654 (2007e:90104)", MRreviewer = "Uwe Sch{\"a}fer", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", 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, pages = "??--??", year = "2008", DOI = "http://dx.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 = "http://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, bookpages = "ix + 237", 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 = "http://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 = "http://dx.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 = "http://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 $Y\,Ax = Yb$, 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", 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 = "http://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 = "http://dx.doi.org/10.1016/j.jco.2009.02.002", ISSN = "0885-064X (print), 1090-2708 (electronic)", MRclass = "41-06", MRnumber = "2524544", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Complexity", } @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 = "http://dx.doi.org/10.1080/10556780802614051", ISSN = "1055-6788", MRclass = "90C30 (65K10 90-08 90C26)", MRnumber = "2554906 (2010i:90116)", bibdate = "Mon Aug 23 19:25:57 2010", bibsource = "http://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", 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 = "http://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 = "http://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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", acknowledgement = ack-nhfb, fjournal = "Optimization Methods and Software", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } %%% ==================================================================== %%% Cross-referenced entries must come last: @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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://www.springerlink.com/content/1385-3139", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://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 = "http://dx.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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 W. Stewart", booktitle = "Impacts of Recent Computer Advances on Operations Research", title = "Impacts of Recent Computer Advances on Operations Research", publisher = pub-NH, address = pub-NH:adr, pages = "xii + 585", year = "1989", ISBN = "0-444-01492-6", ISBN-13 = "978-0-444-01492-4", LCCN = "T57.6 .I4831 1989", bibdate = "Tue May 23 16:35:32 1995", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", series = "Publications in Operations Research", } @Proceedings{Allgower:1990:CSN, editor = "E. L. Allgower and K. Georg", booktitle = "Computational Solution of Nonlinear Systems of Equations", title = "Computational Solution of Nonlinear Systems of Equations", 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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib", series = "Lectures in Applied Mathematics", } @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-NH, address = pub-NH: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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://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", bibdate = "Tue Aug 24 09:08:37 2010", bibsource = "http://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)) }", 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", bibdate = "Tue Aug 24 09:08:37 2010", bibsource = "http://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))", 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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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", MRclass = "65-01 (65G10)", MRnumber = "1386897 (96m:65001)", ISBN-13 = "978-0-7923-3847-5", LCCN = "QA297.75.A66 1996", bibdate = "Mon Oct 20 07:16:07 MDT 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; http://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 = "http://dx.doi.org/10.1007/b96498; http://dx.doi.org/10.1007/978-3-540-21260-7", 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 = "http://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 = "http://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", } %%% Last MathSciNet search: Mon Jan 7 15:24:33 2013