%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "R. Baker Kearfott",
%%%     version         = "2.17",
%%%     date            = "20 June 2014",
%%%     time            = "11:36:37 MDT",
%%%     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        = "13682 4208 19178 199755",
%%%     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 2.17, 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-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-SIAM                = "SIAM"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-SPRINGER-WIEN       = "Spring{\-}er"}
@String{pub-SPRINGER-WIEN:adr   = "Wien / New York"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

%%% ====================================================================
%%% 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 =        "142--150",
  year =         "1983",
  MRclass =      "65K05 (Mathematical programming (numerical methods));
                 65H10 (Systems of nonlinear equations (numerical
                 methods)); 65C99 (Probabilistic methods, simulation and
                 stochastic differential equations (numerical analysis))
                 90C30 (Nonlinear programming); 62J05 (Linear
                 regression)",
  bibdate =      "Fri May 9 19:07:42 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 http://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
  series =       "Lecture Notes in Mathematics",
  ZMnumber =     "0519.65040",
  acknowledgement = ack-nhfb,
  keywords =     "continuation methods; nonlinear least squares;
                 quasi-Newton updates; statistical parameter fitting",
  xxpages =      "140--150",
  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/accesspage/article/10.1007/BF02390516;
                 http://link.springer.com/article/10.1007/BF02390516;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=1&issue=1&spage=3",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://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 G. W. Stewart",
  booktitle =    "Impacts of Recent Computer Advances on Operations
                 Research",
  title =        "Impacts of Recent Computer Advances on Operations
                 Research",
  volume =       "9",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xii + 585",
  year =         "1989",
  ISBN =         "0-444-01492-6",
  ISBN-13 =      "978-0-444-01492-4",
  LCCN =         "T57.6 .I4831 1989",
  bibdate =      "Wed May 28 17:52:37 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Publications in Operations Research",
  URL =          "http://www.zentralblatt-math.org/zmath/en/search/?an=0727.90047",
  ZMnumber =     "0727.90047",
  acknowledgement = ack-nhfb,
  subject =      "Operations research; Data processing",
  tableofcontents = "\\
                 I. Plenary papers \\
                 \\
                 G. B. Dantzig / Decomposition techniques for
                 large-scale electric power systems planning under
                 uncertainty / 3--22 \\
                 \\
                 II. Parallel algorithms for mathematical programming
                 \\
                 \\
                 R. S. Barr, M. G. Christiansen / A parallel auction
                 algorithm: A case study in the use of parallel
                 object-oriented programming, 23--32 \\
                 J. O. Berkey, P. Y. Wang / A comparative study of some
                 parallel bin packing algorithms / 33--43 \\
                 T. E. Gerasch, P. Y. Wang, S. T. Weidman / SIMD
                 knapsack approximation algorithms / 44-- 56 \\
                 A. R. Joshi, D.-S. Chen / A vectorized dual algorithm
                 for generalized network problem / 57--70 \\
                 H. S. Mahmassani, K. C. Mouskos / Vectorization of
                 transportation network equilibrium assignment codes /
                 71--81 \\
                 G. L. Schultz, R. R. Meyer / A flexible parallel
                 algorithm for block-constrained optimization problems /
                 82--91 \\
                 R. Hunter Mladineo / Supercomputers and global
                 optimization / 92--105 \\
                 J. M. Mulvey, H. Vladimirou / Evaluation of a parallel
                 hedging algorithm for stochastic network programming /
                 106--119 \\
                 D. M. Nicol / Parallel solution of dynamic programming
                 equation using optimistic evaluation / 120--130 \\
                 P. M. Pardalos, G. P. Rodgers / Parallel branch and
                 bound algorithms for unconstrained quadratic zero-one
                 programming / 131--143 \\
                 G. Plateau, C. Roucairol / A supercomputer algorithm
                 for the 0--1 multiknapsack problem / 144--157 \\
                 M. J. Saltzman, R. Subramanian, R. E. Marsten /
                 Implementing an interior point LP algorithm on a
                 supercomputer / 158--168 \\
                 C. Phillips, S. A. Zenios / Experiences with large
                 scale network optimization on the connection machine /
                 169--182 \\
                 \\
                 III. Graphics in optimization \\
                 \\
                 I. Lustig / Application of interactive computer
                 graphics to linear programming / 183--189 \\
                 C. L. Monma, D. F. Shallcross / A PC-based interactive
                 network design system for fiber optic communication
                 networks / 190--204 \\
                 \\
                 IV. Microcomputers in operations research \\
                 \\
                 E. Gelman, M. A. Pollatschek / Personal computer
                 version of nearly triangular Leontief LP solution /
                 205--216 \\
                 T. P. Harrison, J. L. Martin / Optimizing exchange
                 agreements in the refining industry / 217-- 225 \\
                 J. K. Ho / Nonprocedural implementation of mathematical
                 programming algorithms / 226--237 \\
                 R. Terry, D. DeBald, R. Chikkala / Closed queueing
                 network analysis of indirect labor requirements /
                 238--247 \\
                 M. L. Villanueva, N. A. Wittpenn, C. B. Austin, E.
                 Baker / A microcomputer-based marine geographic
                 information system with marketing application /
                 248--262 \\
                 E. Wasil, B. Golden, R. Sharda / Mathematical
                 programming software for the microcomputer: Recent
                 advances, comparisons and trends / 263--272 \\
                 E. Wasil, A. Assad / Project management software for
                 the microcomputer: Recent advances and future
                 directions / 273--288 \\
                 \\
                 V. Artificial intelligence and expert systems \\
                 \\
                 G. Anandalingam, R. Mathieu, C. L. Pittard, N. Sinha /
                 Artificial intelligence based approaches for solving
                 hierarchical optimization problems / 289--301 \\
                 J. W. Denton, G. R. Madey / Impact of neurocomputing on
                 operations research / 302--312 \\
                 H. J. Greenberg / Neural networks for an intelligent
                 mathematical programming system / 313-- 320 \\
                 M. R. Hilliard, G. E. Liepins, M. Palmer, G. Rangarajan
                 / The computer as a partner in algorithmic design:
                 Automated discovery of parameters for a multi-objective
                 scheduling heuristic / 321--331 \\
                 J.- Y. Potvin, S. F. Smith / Flexible systems for the
                 design of heuristic algorithms in complex OR domains /
                 332--346 \\
                 \\
                 VI. Vehicle routing and scheduling applications \\
                 \\
                 D. Jovanovic, P. T. Harker / SCAN: A decision support
                 system for railroad scheduling / 347--360 \\
                 K. E. Nygard, P. Juell, K. Nagesh / An interactive
                 decision support system for vehicle routing / 361--372
                 \\
                 J. R. Schaffer, P. K. Pearl / Vehicle routing and
                 scheduling for home delivery / 373--384 \\
                 \\
                 VII. Simulation \\
                 \\
                 O. Balci, R. E. Nance / Simulation model development:
                 The multidimensionality of the computing technology
                 pull / 385--395 \\
                 R. K. Kincaid, K. W. Miller, S. K. Park / Locating P
                 mobile servers on a congested network: A simulation
                 analysis / 396--406 \\
                 R. L. Moose, R. E. Nance / The design and development
                 of an analyzer for discrete event model specifications
                 / 407--421 \\
                 R. J. Paul / Visual simulation: Seeing is believing?
                 422--432 \\
                 M. B. Silberholz, B. L. Golden, E. K. Baker /
                 Simulating a marine container terminal on the Macintosh
                 II / 433 \\
                 \\
                 VIII. Model development and analysis systems \\
                 \\
                 G. H. Bradley / Mathematical programming modeling
                 project - overview / 447--462 \\
                 R. G. Brown, J. W. Chinneck, G. M. Karam / Optimization
                 with constraint programming systems / 463--473 \\
                 M. Grauer, S. Albers, M. Frommberger / Concept and
                 first experiences with an object-oriented interface for
                 mathematical programming / 474--483 \\
                 G. Mitra / Tools for modelling support and construction
                 of optimization applications / 484--496 \\
                 A. D. Waren, M. Pechura, L. S. Lasdon / The GRG2 model
                 builder / 497--506 \\
                 S. Zenios, S. S. Nielsen, M. Pinar / On the use of
                 advance architecture computers via high-level modelling
                 languages / 507 \\
                 \\
                 IX. Telecommunications \\
                 \\
                 A. J. Perticone, J. P. Jarvis, D. R. Shier / Evaluation
                 and design of voice telecommunications network /
                 521--532 \\
                 \\
                 X. Numerical analysis \\
                 \\
                 R. Baker Kearfott / Interval arithmetic methods for
                 nonlinear systems and nonlinear optimization: An
                 outline and status / 533--542 \\
                 A. P. Morgan / Polynomial continuation / 543--554 \\
                 L. T. Watson / Modern homotopy methods in optimization
                 / 555--566",
}

@Proceedings{Allgower:1990:CSN,
  editor =       "E. L. Allgower and K. Georg",
  booktitle =    "Computational Solution of Nonlinear Systems of
                 Equations",
  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-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xv + 442",
  year =         "1990",
  ISBN =         "0-444-88693-1",
  ISBN-13 =      "978-0-444-88693-4",
  LCCN =         "QA221 .A64 1990",
  bibdate =      "Tue May 23 16:55:48 1995",
  bibsource =    "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",
}

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