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Date: Thu, 29 Feb 1996 09:05:04 -0600
From: "Kearfott R. Baker" <rbk5287@interval.usl.edu>
Message-Id: <199602291505.AA06544@interval.usl.edu>
To: neum@cma.univie.ac.at
Subject: optimization_book.bib
Status: R

@BOOK{aberth-book,
   AUTHOR = {Aberth, O.},
   TITLE = {Precise Numerical Analysis},
   PUBLISHER ="Wm. C. Brown",
   ADDRESS ="Dubuque, Iowa",
   YEAR = "1988"
}
@ARTICLE{aberth-c++,
   AUTHOR = {Aberth, O. and Schaefer, M.},
   TITLE = {Precise Computation Using Range Arithmetic, via {C++}},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "18",
   NUMBER ="4",
   PAGES ="481--491",
   MONTH ="December",
   YEAR = "1992"
}
@ARTICLE{aberth-degree,
   AUTHOR = {Aberth, O.},
   TITLE = {Computation of Topological Degree using Interval Arithmetic, and Applications},
   JOURNAL = {Math. Comp.},
   VOLUME = "62",
   NUMBER ="205",
   PAGES ="171--178",
   MONTH ="January",
   YEAR = "1994"
}
@BOOK{adams-brainerd-reference,
   AUTHOR = {Adams, J. C. and Brainerd, W. S. and Martin, J. T. and Smith, B. T. and Wagener, J. L.},
   TITLE = {Fortran 90 Handbook -- Complete {ANSI/ISO} Reference},
   PUBLISHER ="Mc-Graw-Hill",
   ADDRESS ="New York",
   YEAR = "1992"
}
@ARTICLE{akyildiz-no-pathologies,
   AUTHOR = {Akyildiz, Y. and Suwaiyel, M. I.},
   TITLE = {No Pathologies for Interval {Newton's} Method},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="1",
   PAGES ="60--72",
   YEAR = "1993"
}
@ARTICLE{alefeld-slopes,
   AUTHOR = {Alefeld, G.},
   TITLE = {Bounding the Slope of Polynomial Operators and Some Applications},
   JOURNAL = {Computing},
   VOLUME = "26",
   PAGES ="227--237",
   YEAR = "1980"
}
@BOOK{alefeld-herzberger,
   AUTHOR = {Alefeld, G. and Herzberger, J.},
   TITLE = {Introduction to Interval Computations},
   PUBLISHER ="Academic Press",
   ADDRESS ="New York",
   YEAR = "1983"
}
@INPROCEEDINGS{alefeld-survey,
   AUTHOR = {Alefeld, G.},
   TITLE = {Inclusion Methods for Systems of Nonlinear Equations -- The Interval Newton Method and Modifications},
   PAGES ="7--26",
   PUBLISHER ="Elsevier Science Publishers",
   BOOKTITLE = {Topics in Validated Computations},
   EDITOR ={J. Herzberger},
   ADDRESS ="Amsterdam",
   YEAR = "1994"
}
@BOOK{alexandroff--hopf,
   AUTHOR = {Alexandroff, P. and Hopf, H.},
   TITLE = {Topologie},
   PUBLISHER ="Chelsea",
   YEAR = "1935"
}
@BOOK{allgower-book,
   AUTHOR = {Allgower, E. and Georg, K.},
   TITLE = {Numerical Continuation Methods: An Introduction},
   PUBLISHER ="Springer-Verlag",
   ADDRESS ="New York",
   YEAR = "1990"
}
@ARTICLE{apostolatos-triplex,
   AUTHOR = {Apostolatos, N. and Kulisch, U. and Krawczyk R. and Lortz, B. and Nickel, K. and Wippermann, H.-W.},
   TITLE = {The Algorithmic Language Triplex-{ALGOL-60}},
   JOURNAL = {Numer. Math.},
   VOLUME = "11",
   PAGES ="175--180",
   YEAR = "1968"
}
@ARTICLE{unicalc,
   AUTHOR = {Babichev, A. B. and Kadyrova, O. B. and Kashevarova, T. P. and Leshchenko, A. S. and Semenov, A. L.},
   TITLE = {UniCalc, a Novel Approach to Solving Systems of Algebraic Equations},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="2",
   PAGES ="29--47",
   YEAR = "1993"
}
@ARTICLE{bailey-f90-mp,
   AUTHOR = {Bailey, D. H.},
   TITLE = {A Fortran 90-Based Multiprecision System},
   JOURNAL = {ACM Trans.\ Math.\ Software},
   VOLUME = "21",
   NUMBER ="4",
   PAGES ="379--387",
   MONTH ="December",
   YEAR = "1995"
}
@ARTICLE{balaji-gritton,
   AUTHOR = {Balaji, G. V. and Seader, J. D.},
   TITLE = {Application of Interval Newton methods to Chemical Engineering Problems},
   JOURNAL = {Reliable Computing},
   VOLUME = "1",
   NUMBER ="3",
   PAGES ="215--223",
   YEAR = "1995"
}
@BOOK{bauch-book,
   AUTHOR = {Bauch, H. and Jahn, K.-U. and {Oelschl\"agel}, D. and {S\"usse}, H. and Wiebigke, V.},
   TITLE = {Intervallmathematik -- Theorie und Anwendungen},
   PUBLISHER ="Teubner",
   ADDRESS ="Leipzig",
   YEAR = "1987"
}
@ARTICLE{baumann-centers,
   AUTHOR = {Baumann, E.},
   TITLE = {Optimal Centered Forms},
   JOURNAL = {BIT},
   VOLUME = "28",
   NUMBER ="1",
   PAGES ="80--87",
   YEAR = "1988"
}
@ARTICLE{intervall-fortran,
   AUTHOR = {Bendzulla, C.},
   TITLE = {The {INTERVALL-FORTRAN} Compilers},
   JOURNAL = {Rechentech. Datenverarb.},
   VOLUME = "17",
   NUMBER ="11",
   PAGES ="10-12",
   YEAR = "1980"
}
@ARTICLE{benhamou,
   AUTHOR = {Benhamou, F. and Older, W. J.},
   TITLE = {Applying Interval Arithmetic to Real, Integer, and Boolean Constraints},
   JOURNAL = {Journal of Mathematics and Mechanics},
   YEAR = "1995"
}
@INPROCEEDINGS{berner-scan,
   AUTHOR = {Berner, S.},
   TITLE = {A Parallel Method for Verified Global Optimization},
   PUBLISHER ="Akademie Verlag",
   BOOKTITLE = {Scientific Computing and Validated Numerics},
   EDITOR ={G. Alefeld and A. Frommer},
   SERIES ="Mathematical Research",
   ADDRESS ="Berlin",
   YEAR = "1996"
}
@ARTICLE{fortran-sc,
   AUTHOR = {Bleher, J. H. and Rump, S. M. and Kulisch, U. and Metzger, M. and Ullrich, C. and Walter, W.},
   TITLE = {{FORTRAN-SC --- A} Study of a Fortran Extension for Engineering Scientific Computation with Access to {ACRITH}},
   JOURNAL = {Computing},
   VOLUME = "39",
   NUMBER ="2",
   PAGES ="93--110",
   YEAR = "1987"
}
@BOOK{brainerd-guide,
   AUTHOR = {Brainerd, W. S. and Goldberg, C. H. and Adams, J. C.},
   TITLE = {Programmer's Guide to {Fortran 90}},
   PUBLISHER ="Mc-Graw-Hill",
   ADDRESS ="New York",
   YEAR = "1990"
}
@PHDTHESIS{braune-diss,
   AUTHOR = {Braune, K. D.},
   TITLE = {{Hochgenaue Standardfunktionen {f\"ur} reele und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern}},
   SCHOOL ={{Universit\"at Karlsruhe}},
   YEAR = "1987"
}
@ARTICLE{brent-mp,
   AUTHOR = {Brent, R. P.},
   TITLE = {Algorithm 524: {MP}, A {FORTRAN} Multiple-Precision Arithmetic Package},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "4",
   NUMBER ="1",
   PAGES ="71--81",
   MONTH ="March",
   YEAR = "1978"
}
@ARTICLE{brouwer-fixed-point,
   AUTHOR = {Brouwer, L. E. J.},
   TITLE = {{\"Uber Abbildung von Mannigfaltigkeiten}},
   JOURNAL = {Math. Ann.},
   VOLUME = "71",
   PAGES ="97--115",
   YEAR = "1912"
}
@ARTICLE{browder-degree-summary,
   AUTHOR = {Browder, F. E.},
   TITLE = {Fixed Point Theory and Nonlinear Problems},
   JOURNAL = {Bull. Amer. Math. Soc.},
   VOLUME = "9",
   NUMBER ="1",
   PAGES ="1--39",
   MONTH ="July",
   BOOKTITLE = {Presented at the Symposium on the Mathematical Heritage of Henri Poin},
   YEAR = "1983"
}
@ARTICLE{bundy-int,
   AUTHOR = {Bundy, A.},
   TITLE = {A Generalized Interval Package and its Use for Semantic Checking},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "10",
   NUMBER ="4",
   PAGES ="397--409",
   PUBLISHER ="ACM",
   YEAR = "1984"
}
@ARTICLE{caprani-real-valued,
   AUTHOR = {Caprani, O. and Godthaab, B. and Madsen, K.},
   TITLE = {Use of a Real-Valued Local Minimum in Parallel Interval Global Optimization},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="2",
   PAGES ="71--82",
   YEAR = "1993"
}
@ARTICLE{chen-optimal-krawczyk,
   AUTHOR = {Chen, X. AND  Wang, D.},
   TITLE = {On the Optimal Properties of the Krawczyk-Type Interval Operator},
   JOURNAL = {Internat. J. Comput. Math.},
   VOLUME = "29",
   NUMBER ="2-4",
   PAGES ="235-45",
   YEAR = "1989"
}
@INPROCEEDINGS{van-emden-subsit,
   AUTHOR = {Chen, H. M. and van Emden, M. H.},
   TITLE = {Adding Interval Constraints to the {Moore--Skelboe} Global Optimization Algorithm},
   JOURNAL = {Reliable Computing (Supplement)},
   PAGES ="54--57",
   PUBLISHER ="Reliable Computing (Supplement)",
   BOOKTITLE = {Extended Abstracts of APIC'95, International Workshop on Applications of Interval Computations},
   EDITOR ={V. Kreinovich},
   YEAR = "1995"
}
@BOOK{cody-software-manual,
   AUTHOR = {Cody, W. J. and Waite, W.},
   TITLE = {Software Manual for the Elementary Functions},
   PUBLISHER ="Prentice-Hall",
   ADDRESS ="Englewood Cliffs, NJ",
   YEAR = "1980"
}
@ARTICLE{triplex-algol,
   AUTHOR = {Cole, A. J. and Morrison, R.},
   TITLE = {Triplex:  A System for Interval Arithmetic},
   JOURNAL = {Software - Practice and Experience},
   VOLUME = "12",
   PAGES ="341--350",
   YEAR = "1982"
}
@ARTICLE{more-coleman,
   AUTHOR = {Coleman, T. F. and {Mor\'e}, J. J.},
   TITLE = {Estimation of Sparse Jacobian matrices and Graph Coloring Problems},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "20",
   PAGES ="187--209",
   YEAR = "1984"
}
@BOOK{lancelot-doc,
   AUTHOR = {Conn, A. R. and Gould, N. and Toint, Ph.L.},
   TITLE = {{LANCELOT}: A Fortran Package for Large-Scale Nonlinear Optimization},
   PUBLISHER ="Springer-Verlag",
   SERIES ="Series in Computational Mathematics, vol. 17",
   ADDRESS ="New York",
   YEAR = "1992"
}
@ARTICLE{connell-corless-maple,
   AUTHOR = {Connell, A. and Corless, R. M.},
   TITLE = {An Experimental Interval Arithmetic Package in {Maple}},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="2",
   PAGES ="120--134",
   YEAR = "1993"
}
@MISC{corliss-bias-proposal,
   AUTHOR = {Corliss, G. F.},
   TITLE = {Proposal for a Basic Interval Arithmetic Subroutines Library {(BIAS)}},
NOTE={Preprint, Dept. of Math., Stat. and Comp. Sci., Marquette Univ., Milwaukee, WI 53233},
   YEAR = "1990"
}
@INPROCEEDINGS{corliss-ada,
   AUTHOR = {Corliss, G. F. and Rall, L. B.},
   TITLE = {Computing the Range of Derivatives},
   VOLUME = "12",
   PAGES ="195--212",
   PUBLISHER ="J. C. Baltzer AG",
   BOOKTITLE = {Computer Arithmetic, Scientific Computation, and Mathematical Modelling},
   EDITOR ={Kaucher, E. and Markov, S. M. and Mayer, G.},
   SERIES ="{IMACS} Annals on Computing and Applied Math.",
   ADDRESS ="Basel",
   YEAR = "1991"
}
@MISC{corliss-intarith-comparisons,
   AUTHOR = {Corliss, G. F.},
   TITLE = {Comparing Software Packages for Interval Arithmetic},
NOTE={Talk given at IMACS / GAMM International Symposium (SCAN'93), Vienna, Austria, Sept. 26 -- 29, 1993},
   YEAR = "1993"
}
@INPROCEEDINGS{corliss-leichester,
   AUTHOR = {Corliss, G. F.},
   TITLE = {Guaranteed Error Bounds for Ordinary Differential Equations},
   BOOKTITLE = {Lecture notes for the VI-th SERC Numerical Analysis Summer School, Leichester University, July 25--29},
   YEAR = "1994"
}
@ARTICLE{cornelius-lohner,
   AUTHOR = {Cornelius, H. and Lohner, R.},
   TITLE = {Computing the Range of Values of Real Functions with Accuracy Higher than Second Order},
   JOURNAL = {Computing},
   VOLUME = "33",
   NUMBER ="3",
   PAGES ="331--347",
   YEAR = "1984"
}
@TECHREPORT{crary-augment,
   AUTHOR = {Crary, F.},
   TITLE = {The {AUGMENT} Precompiler},
   INSTITUTION ="MRC, University of Wisconsin, Madison",
   NUMBER ="1470",
   YEAR = "1976"
}
@BOOK{cronin-degree,
   AUTHOR = {Cronin, J.},
   TITLE = {Fixed Points and Topological Degree in Nonlinear Analysis},
   PUBLISHER ="American Mathematical Society",
   ADDRESS ="Providence, RI",
   YEAR = "1964"
}
@MISC{csallner-scan,
   AUTHOR = {Csallner, A. E. and Csendes, T.},
   TITLE = {Convergence Speed of Interval Methods for Global Optimization and the Joint Effects of Algorithmic Modifications},
NOTE={Talk given at SCAN'95, Wuppertal, Germany, Sept. 26 -- 29, 1995},
   YEAR = "1995"
}
@ARTICLE{csendes-quasi-newton,
   AUTHOR = {Csendes, T.},
   TITLE = {Nonlinear Parameter Estimation by Global Optimization -- Efficiency and Reliability},
   JOURNAL = {Acta Cybernetica},
   VOLUME = "8",
   NUMBER ="4",
   PAGES =" 361--370",
   YEAR = "1988"
}
@MISC{csendes-siam-subdivision,
   AUTHOR = {Csendes, T. and Ratz, D.},
   TITLE = {Subdivision Direction Selection in Interval Methods for Global Optimization},
NOTE={Accepted for publication in {\it SIAM J. Numer. Anal.}},
   YEAR = "1994"
}
@BOOK{dennis-schnabel-book,
   AUTHOR = {Dennis, J. E. and Schnabel, R. B.},
   TITLE = {Numerical Methods for Unconstrained Optimization and Nonlinear Least Squares},
   PUBLISHER ="Prentice-Hall",
   ADDRESS ="Englewood Cliffs, NJ",
   YEAR = "1983"
}
@INPROCEEDINGS{dixon-szego,
   AUTHOR = {Dixon, L. C. W. and {Szeg\"o}, G. P.},
   TITLE = {The Global Optimization Problem: An Introduction},
   PAGES ="1--15",
   PUBLISHER ="North-Holland",
   BOOKTITLE = {Towards Global Optimization 2},
   EDITOR ={Dixon, L. C. W. and {Szeg\"o}, G. P.},
   ADDRESS ="Amsterdam, Netherlands",
   YEAR = "1978"
}
@ARTICLE{dongarra-netlib,
   AUTHOR = {Dongarra, J. J. and  Grosse, E.},
   TITLE = {Distribution of Mathematical Software Via Electronic Mail},
   JOURNAL = {Comm. ACM},
   VOLUME = "30",
   NUMBER ="5",
   PAGES ="403--407",
   MONTH ="May",
   YEAR = "1987"
}
@ARTICLE{du-univariate-cluster,
   AUTHOR = {Du, K. and Kearfott, R. B.},
   TITLE = {The Cluster Problem in Global Optimization The Univariate Case},
   JOURNAL = {Computing (Suppl.)},
   VOLUME = "9",
   PAGES ="117--127",
   YEAR = "1992"
}
@PHDTHESIS{du-diss,
   AUTHOR = {Du, K.},
   TITLE = {Cluster Problem in Global Optimization using Interval Arithmetic},
   SCHOOL ={{University of Southwestern Louisiana}},
   YEAR = "1994"
}
@ARTICLE{ely-vpi,
   AUTHOR = {Ely, J. S.},
   TITLE = {The {VPI} Software Package for Variable Precision Interval Arithmetic},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="2",
   PAGES ="135--153",
   YEAR = "1993"
}
@ARTICLE{enger-ray-tracing,
   AUTHOR = {Enger, W.},
   TITLE = {Interval Ray Tracing -- A Divide and Conquer Strategy for Realistic Computer Graphics},
   JOURNAL = {The Visual Computer},
   VOLUME = "9",
   PAGES ="91--104",
   YEAR = "1992"
}
@PHDTHESIS{eriksson-diss-parallel,
   AUTHOR = {Eriksson, J.},
   TITLE = {Parallel Global Optimization using Interval Analysis},
   SCHOOL ={{University of {Ume\aa}}},
   ADDRESS ="Institute of Information Processing",
   YEAR = "1991"
}
@ARTICLE{eriksson-ic-article,
   AUTHOR = {Eriksson, J and  {Lindstr{\oe}m}, P.},
   TITLE = {A Parallel Interval Method Implementation for Global Optimization Using Dynamic Load Balancing},
   JOURNAL = {Reliable Computing},
   VOLUME = "1",
   NUMBER ="1",
   PAGES ="77-92",
   YEAR = "1995"
}
@BOOK{floudas-pardalos-test-set,
   AUTHOR = {Floudas, C. A. and Pardalos, P. M.},
   TITLE = {A Collection of Test Problems for Constrained Global Optimization Algorithms},
   PUBLISHER ="Springer-Verlag",
   SERIES ="Lecture Notes in Computer Science no. 455",
   ADDRESS ="New York",
   YEAR = "1990"
}
@ARTICLE{henrici-disk-arithmetic,
   AUTHOR = {Gargantini, J. and Henrici, P.},
   TITLE = {Circular Arithmetic and the Determination of Polynomial Zeros},
   JOURNAL = {Numer. Math.},
   VOLUME = "18",
   PAGES ="305--320",
   YEAR = "1972"
}
@BOOK{gill-murray-wright,
   AUTHOR = {Gill, P. E. and Murray, W. and Wright, M.},
   TITLE = {Practical Optimization},
   PUBLISHER ="Academic Press",
   ADDRESS ="New York",
   YEAR = "1981"
}
@BOOK{golub-van-loan,
   AUTHOR = {Golub, G. H. and Van Loan, C. F.},
   TITLE = {Matrix Computations (Second Edition)},
   PUBLISHER ="Johns Hopkins University Press",
   ADDRESS ="Baltimore, MD",
   YEAR = "1989"
}
@BOOK{matrix-test-set,
   AUTHOR = {Gregory, R. T. and Karney, D. L},
   TITLE = {A Collection of Matrices for Testing Computational Algorithms},
   PUBLISHER ="Wiley",
   ADDRESS ="New York",
   YEAR = "1969"
}
@INPROCEEDINGS{griewank-toint-separable,
   AUTHOR = {Griewank, A. and Toint, Ph. L.},
   TITLE = {On the Unconstrained Optimization of Partially Separable Functions},
   PAGES ="301--312",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Nonlinear Optimization 1981},
   EDITOR ={Powell, M. J. D.},
   ADDRESS ="New York",
   YEAR = "1982"
}
@ARTICLE{griewank-news1,
   AUTHOR = {Griewank, A.},
   TITLE = {The Chain Rule Revisited in Scientific Computing},
   JOURNAL = {SIAM News},
   VOLUME = "24",
   NUMBER ="3",
   PAGES ="20--21",
   MONTH ="May",
   YEAR = "1991"
}
@ARTICLE{griewank-news2,
   AUTHOR = {Griewank, A.},
   TITLE = {The Chain Rule Revisited in Scientific Computing},
   JOURNAL = {SIAM News},
   VOLUME = "24",
   NUMBER ="4",
   PAGES ="8--24",
   MONTH ="July",
   YEAR = "1991"
}
@PROCEEDINGS{griewank-proceedings,

   TITLE = {Automatic Differentiation of Algorithms: Theory, Implementation, and Application},
   PUBLISHER ="SIAM",
   EDITOR ={Griewank, A. and Corliss, G. F.},
   ADDRESS ="Philadelphia",
   YEAR = "1991"
}
@INPROCEEDINGS{griewank-markowitz,
   AUTHOR = {Griewank, A. and Reese, S.},
   TITLE = {On the Calculation of Jacobian Matrices by the Markowitz Rule},
   PAGES ="126--135",
   PUBLISHER ="SIAM",
   BOOKTITLE = {Automatic Differentiation of Algorithms:  Theory, Implementation, and Application},
   EDITOR ={Griewank, A. and Corliss, G. F.},
   ADDRESS ="Philadelphia",
   YEAR = "1991"
}
@ARTICLE{grosse-netlib,
   AUTHOR = {Grosse, E. and Dongarra, J. J.},
   TITLE = {Distribution of Mathematical Software via Electronic Mail},
   JOURNAL = {SIGNUM Newsletter},
   VOLUME = "20",
   NUMBER ="3",
   PAGES ="45--47",
   MONTH ="July",
   PUBLISHER ="SIAM",
   YEAR = "1985"
}
@ARTICLE{hager-ic-constraints,
   AUTHOR = {Hager, G. D.},
   TITLE = {Solving Large Systems of Nonlinear Constraints with Application to Data Modeling},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="2",
   PAGES ="169--200",
   YEAR = "1993"
}
@INPROCEEDINGS{pascal-xsc,
   AUTHOR = {Hammer, R. and  Neaga, M. and  Ratz, D.},
   TITLE = {{PASCAL-XSC, New} Concepts for Scientific Computation and Numerical Data Processing},
   PAGES ="15--44",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Scientific Computing with Automatic Result Verification},
   EDITOR ={Adams, E. and Kulisch, U.},
   ADDRESS ="New York, etc.",
   YEAR = "1993"
}
@BOOK{hammer-book,
   AUTHOR = {Hammer, R. and Hocks, M. and Kulisch, U. and Ratz, D.},
   TITLE = {Numerical Toolbox for Verified Computing {I}},
   PUBLISHER ="Springer-Verlag",
   ADDRESS ="New York",
   YEAR = "1993"
}
@ARTICLE{hansen-ge,
   AUTHOR = {Hansen, E. R.},
   TITLE = {Interval Arithmetic in Matrix Computations, Part 1},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "2",
   PAGES ="308--320",
   YEAR = "1965"
}
@ARTICLE{hansen-slope,
   AUTHOR = {Hanson, E. R.},
   TITLE = {Interval Forms of {Newton's} Method},
   JOURNAL = {Computing},
   VOLUME = "20",
   PAGES ="153--163",
   YEAR = "1978"
}
@ARTICLE{hansen-1d,
   AUTHOR = {Hansen, E. R.},
   TITLE = {Global Optimization Using Interval Analysis: The One-Dimensional Case},
   JOURNAL = {J. Optim. Theory Appl.},
   VOLUME = "29",
   NUMBER ="3",
   PAGES ="331-44",
   YEAR = "1979"
}
@ARTICLE{hansen-multidim-in,
   AUTHOR = {Hansen, E. R.},
   TITLE = {Global Optimization Using Interval Analysis:  the Multidimensional Case},
   JOURNAL = {Numer. Math.},
   VOLUME = "34",
   NUMBER ="3",
   PAGES ="247--270",
   PUBLISHER ="Springer",
   YEAR = "1980"
}
@ARTICLE{hansen-greenberg,
   AUTHOR = {Hansen, E. R. and Greenberg, R. I.},
   TITLE = {An Interval Newton Method},
   JOURNAL = {Appl. Math. Comput.},
   VOLUME = "12",
   PAGES ="89--98",
   YEAR = "1983"
}
@BOOK{hansen-book,
   AUTHOR = {Hansen, E. R.},
   TITLE = {Global Optimization Using Interval Analysis},
   PUBLISHER ="Marcel Dekker, Inc.",
   ADDRESS ="New York",
   YEAR = "1992"
}
@ARTICLE{hansen-linsys-bounds,
   AUTHOR = {Hansen, E. R.},
   TITLE = {Bounding the Solution of Interval Linear Equations},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "29",
   NUMBER ="5",
   PAGES ="1493--1503",
   MONTH ="October",
   YEAR = "1992"
}
@ARTICLE{hansen-walster-multipliers,
   AUTHOR = {Hansen, E. R. and Walster, G. W.},
   TITLE = {Bounds for {Lagrange} Multipliers and Optimal Points},
   JOURNAL = {Comput. Math. Appl.},
   VOLUME = "25",
   NUMBER ="10",
   PAGES ="59",
   YEAR = "1993"
}
@ARTICLE{heinz-degree,
   AUTHOR = {Heinz, E.},
   TITLE = {An Elementary Analytic Theory of the Degree of Mapping in {$n$}-Dimensional Space},
   JOURNAL = {Journal of Mathematics and Mechanics},
   VOLUME = "8",
   NUMBER ="2",
   PAGES ="231--247",
   YEAR = "1959"
}
@ARTICLE{herzberger-algol60,
   AUTHOR = {Herzberger, J.},
   TITLE = {{ALGOL-60} Procedures Evaluating Standard Functions in Interval Analysis},
   JOURNAL = {Computing},
   VOLUME = "5",
   NUMBER ="4",
   PAGES ="377--384",
   YEAR = "1970"
}
@PROCEEDINGS{herzberger-topics,

   TITLE = {Topics in Validated Computations},
   PUBLISHER ="Elsevier Science Publishers",
   BOOKTITLE = {Topics in Validated Computations},
   EDITOR ={J. Herzberger},
   SERIES ="Studies in Computational Mathematics",
   ADDRESS ="Amsterdam",
   YEAR = "1994"
}
@BOOK{globopt-handbook,
   AUTHOR = {Horst, R. and Pardalos, M., eds.},
   TITLE = {Handbook of Global Optimization},
   PUBLISHER ="Kluwer",
   ADDRESS ="Dordrecht, Netherlands",
   YEAR = "1995"
}
@PHDTHESIS{hudiss,
   AUTHOR = {Hu, C.},
   TITLE = {Optimal Preconditioners for the Interval Newton Method},
   SCHOOL ={{University of Southwestern Louisiana}},
   YEAR = "1990"
}
@ARTICLE{hu-inverse-trig-hyperbolic,
   AUTHOR = {Hu, C. and Kearfott, R. B.},
   TITLE = {On Bounding the Range of Some Elementary Functions in {FORTRAN 77}},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="3",
   PAGES ="29--39",
   YEAR = "1993"
}
@TECHREPORT{TPX,
   AUTHOR = {Husung, D.},
   TITLE = {Precompiler for Scientific Computation {(TPX)}},
   INSTITUTION ="Inst. for Comp. Sci. III, Technical University Hamburg--Harburg",
   NUMBER ="91.1",
   YEAR = "1989"
}
@TECHREPORT{incpp,
   AUTHOR = {{Hyv\"onen}, E. and De Pascale, S.},
   TITLE = {Interval Constraint Satisfaction Tool {InC++}: A Local Interval Arithmetic Library},
   INSTITUTION ="VTT, Tech. Research Center of Finland",
   YEAR = "1994"
}
@INPROCEEDINGS{hyvonen-el-paso,
   AUTHOR = {{Hyv\"onen}, E. and De Pascale, S.},
   TITLE = {Interval Computations on the Spreadsheet},
   PUBLISHER ="Kluwer",
   BOOKTITLE = {Applications of Interval Computations},
   EDITOR ={R. B. Kearfott and V. Kreinovich},
   SERIES ="Applied Optimization",
   ADDRESS ="Dordrecht, Netherlands",
   YEAR = "1995"
}
@INPROCEEDINGS{hyvonen-wuppertal,
   AUTHOR = {{Hyv\"onen}, E. and {De Pascale}, S.},
   TITLE = {Shared Computations for Efficient Interval Function Evaluation},
   PUBLISHER ="Akademie Verlag",
   BOOKTITLE = {Scientific Computing and Validated Numerics},
   EDITOR ={G. Alefeld and A. Frommer},
   SERIES ="Mathematical Research",
   ADDRESS ="Berlin",
   YEAR = "1996"
}
@ARTICLE{ichida-algorithm,
   AUTHOR = {Ichida, K. and Fujii, Y.},
   TITLE = {An Interval Arithmetic Method for Global Optimization},
   JOURNAL = {Computing},
   VOLUME = "23",
   NUMBER ="1",
   PAGES ="85-97",
   YEAR = "1979"
}
@ARTICLE{iri-original,
   AUTHOR = {Iri, M.},
   TITLE = {Simultaneous Computation of Functions, Partial Derivatives and Estimates of Rounding Errors -- Complexity and Practicality --},
   JOURNAL = {Japan Journal of Applied Mathematics},
   VOLUME = "1",
   NUMBER ="2",
   PAGES ="223--252",
   MONTH ="December",
   YEAR = "1984"
}
@TECHREPORT{iri-review,
   AUTHOR = {Iri, M. and Kubota, K.},
   TITLE = {Methods of Fast Automatic Differentiation and Applications},
   MONTH ="July",
   INSTITUTION ="University of Tokyo",
   NUMBER ="RMI 87-02",
   YEAR = "1987"
}
@PHDTHESIS{jan-diss,
   AUTHOR = {Jan, C.-H.},
   TITLE = {Expression Parsing and Rigorous Computation of Bounds on All Solutions to Practical Nonlinear Systems},
   MONTH ="May",
   SCHOOL ={{University of Southwestern Louisiana}},
   YEAR = "1992"
}
@ARTICLE{jansen-acrith,
   AUTHOR = {Jansen, P. and Weidner, P.},
   TITLE = {High-Accuracy Arithmetic Software -- Some Tests of the {ACRITH} Problem Solving Routines},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "12",
   NUMBER ="1",
   PAGES ="62--71",
   YEAR = "1986"
}
@TECHREPORT{jansson-1d,
   AUTHOR = {Jansson, C.},
   TITLE = {A Global Minimization Method: The One-Dimensional Case},
   MONTH ="November",
   INSTITUTION ="Technical University Hamburg-Harburg",
   NUMBER ="91.2",
   YEAR = "1991"
}
@INPROCEEDINGS{jansson-nd,
   AUTHOR = {Jansson, C.},
   TITLE = {A Global Optimization Method Using Interval Arithmetic},
   PAGES ="259--268",
   PUBLISHER ="North-Holland",
   BOOKTITLE = {Computer Arithmetic and Enclosure Methods},
   EDITOR ={L. Atanassova and J. Herzberger},
   ADDRESS ="Amsterdam, Netherlands",
   YEAR = "1992"
}
@INPROCEEDINGS{jansson-survey,
   AUTHOR = {Jansson, C.},
   TITLE = {On Self-Validating Methods for Optimization Problems},
   PAGES ="381--439",
   PUBLISHER ="North-Holland",
   BOOKTITLE = {Topics in Validated Computations},
   EDITOR ={J. Herzberger},
   ADDRESS ="Amsterdam, Netherlands",
   YEAR = "1994"
}
@TECHREPORT{jansson-knueppel-tests,
   AUTHOR = {Jansson, C. and {Kn\"uppel}, O.},
   TITLE = {Numerical Results for a Self-Validating Global Optimization Method},
   MONTH ="February",
   INSTITUTION ="Technical University Hamburg--Harburg",
   NUMBER ="94.1",
   YEAR = "1994"
}
@ARTICLE{jeter-shriver,
   AUTHOR = {Jeter, J. P. and  Shriver, B. D.},
   TITLE = {Variable Precision and Interval Arithmetic: A Portable Enhancement to {FORTRAN}},
   JOURNAL = {Adv. Eng. Software},
   VOLUME = "6",
   NUMBER ="1",
   PAGES ="45--50",
   YEAR = "1984"
}
@TECHREPORT{bibins,
   AUTHOR = {{J\"ullig}, H.-P.},
   TITLE = {{Algorithmen mit Ergebnisverification mit {C++/2.0}}},
   INSTITUTION ="Technical University Hamburg-Harburg",
   YEAR = "1991"
}
@INPROCEEDINGS{kahan-arithmetic-notes,
   AUTHOR = {Kahan, W. M.},
   TITLE = {A More Complete Interval Arithmetic},
   BOOKTITLE = {Lecture Notes for a Summer Course at the University of Michigan},
   YEAR = "1968"
}
@BOOK{kaucher-miranker,
   AUTHOR = {Kaucher, E. W. and Miranker, W. L.},
   TITLE = {Self-Validating Numerics for Function Space Problems},
   PUBLISHER ="Academic Press",
   ADDRESS ="Orlando",
   YEAR = "1984"
}
@PROCEEDINGS{kaucher-1987-proceedings,

   TITLE = {Computer Arithmetic -- Scientific Computation and Programming Languages},
   PUBLISHER ="Teubner",
   BOOKTITLE = {Computer Arithmetic -- Scientific Computation and Programming Languages},
   EDITOR ={Kaucher, E. and Kulisch, U. and Ullrich, Ch.},
   ADDRESS ="Stuttgart",
   YEAR = "1987"
}
@PHDTHESIS{kearfott-diss,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Computing the Degree of Maps and a Generalized Method of Bisection},
   SCHOOL ={{University of Utah}},
   ADDRESS ="Department of Mathematics",
   YEAR = "1977"
}
@ARTICLE{kearfott-numer-math,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {An Efficient Degree-Computation Method for a Generalized Method of Bisection},
   JOURNAL = {Numer. Math.},
   VOLUME = "32",
   PAGES ="109--127",
   YEAR = "1979"
}
@ARTICLE{abstbis,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Abstract Generalized Bisection and a Cost Bound},
   JOURNAL = {Math. Comp.},
   VOLUME = "49",
   NUMBER ="179",
   PAGES ="187--202",
   MONTH ="July",
   YEAR = "1987"
}
@ARTICLE{bis-tests,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Some Tests of Generalized Bisection},
   JOURNAL = {ACM Trans.\ Math.\ Software},
   VOLUME = "13",
   NUMBER ="3",
   PAGES ="197--220",
   MONTH ="September",
   YEAR = "1987"
}
@INPROCEEDINGS{ams-siam-review,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Interval Arithmetic Techniques in the Computational Solution of Nonlin ear Systems of Equations:  Introduction, Examples, and Comparisons},
   PAGES ="337--358",
   PUBLISHER ="American Mathematical Society",
   BOOKTITLE = { Computational Solution of Nonlinear Systems of Equations (Lectures in Applied Mathematics, volume 26)},
   EDITOR ={E. L. Allgower and K. Georg},
   ADDRESS ="Providence, RI",
   YEAR = "1990"
}
@ARTICLE{singbis,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Interval {Newton} / Generalized Bisection When There are Singularities near Roots},
   JOURNAL = {Annals of Operations Research},
   VOLUME = "25",
   PAGES ="181--196",
   YEAR = "1990"
}
@ARTICLE{siam-precond,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Preconditioners for the Interval {Gauss--Seidel} Method},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "27",
   NUMBER ="3",
   PAGES ="804--822",
   MONTH ="June",
   YEAR = "1990"
}
@ARTICLE{intbis,
   AUTHOR = {Kearfott, R. B. and Novoa, M.},
   TITLE = {Algorithm 681: {INTBIS}, A Portable Interval {Newton}/Bisection Package},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "16",
   NUMBER ="2",
   PAGES ="152--157",
   MONTH ="June",
   PUBLISHER ="Univ. of Southwestern Louisiana",
   YEAR = "1990"
}
@ARTICLE{computing-decomposition,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Decomposition of Arithmetic Expressions to Improve the Behavior of Interval Iteration for Nonlinear Systems},
   JOURNAL = {Computing},
   VOLUME = "47",
   NUMBER ="2",
   PAGES ="169--191",
   YEAR = "1991"
}
@ARTICLE{ic-precond-review,
   AUTHOR = {Kearfott, R. B. and Hu, C. and Novoa, M.},
   TITLE = {A Review of Preconditioners for the Interval {Gauss--Seidel} Method},
   JOURNAL = {Interval Computations},
   VOLUME = "1",
   NUMBER ="1",
   PAGES ="59--85",
   YEAR = "1991"
}
@ARTICLE{kearfott-bound-constrained,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {An Interval Branch and Bound Algorithm for Bound Constrained Optimization Problems},
   JOURNAL = {Journal of Global Optimization},
   VOLUME = "2",
   PAGES ="259--280",
   EDITOR ={Panos Pardalos et al},
   YEAR = "1992"
}
@ARTICLE{intlib-moscow,
   AUTHOR = {Kearfott,  R. B. and Dawande, M. and Du K.-S. and Hu, C.},
   TITLE = {{INTLIB}:  A Portable {FORTRAN 77} Elementary Function Library},
   JOURNAL = {Interval Computations},
   VOLUME = "3",
   NUMBER ="5",
   PAGES ="96--105",
   YEAR = "1992"
}
@MISC{xing-surface-patch-intersection,
   AUTHOR = {Kearfott, R. B. and Xing, Z.},
   TITLE = {Rigorous Computation of Surface Patch Intersection Curves},
NOTE={Preprint, Department of Mathematics, Univ. of Southwestern Louisiana, U.S.L. Box 4-1010, Lafayette, LA 70504},
   YEAR = "1993"
}
@MISC{empirical-eval,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Algebraic Systems},
NOTE={Accepted for publication in {\it SIAM J. Sci. Comput.}},
   YEAR = "1994"
}
@MISC{opt-review,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems},
NOTE={Preprint, Department of Mathematics, Univ. of Southwestern Louisiana, U.S.L. Box 4-1010, Lafayette, LA 70504},
   YEAR = "1994"
}
@MISC{verifying-feasibility,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {On Proving Existence of Feasible Points in Equality Constrained Optimization Problems},
NOTE={Preprint, Department of Mathematics, Univ. of Southwestern Louisiana, U.S.L. Box 4-1010, Lafayette, LA 70504},
   YEAR = "1994"
}
@TECHREPORT{feasibility-report,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {On Verifying Feasibility in Equality Constrained Optimization Problems},
   INSTITUTION ="University of Southwestern Louisiana",
   YEAR = "1994"
}
@ARTICLE{siam-step-control,
   AUTHOR = {Kearfott, R. B. and Xing, Z.},
   TITLE = {An Interval Step Control for Continuation Methods},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "31",
   NUMBER ="3",
   PAGES ="892--914",
   MONTH ="June",
   YEAR = "1994"
}
@ARTICLE{multivariate-cluster,
   AUTHOR = {Kearfott, R. B. and Du, K.},
   TITLE = {The Cluster Problem in Multivariate Global Optimization},
   JOURNAL = {Journal of Global Optimization},
   VOLUME = "5",
   PAGES ="253--265",
   YEAR = "1994"
}
@ARTICLE{intlib,
   AUTHOR = {Kearfott,  R. B. and Dawande, M. and Du, K.-S. and Hu, C.-Y.},
   TITLE = {Algorithm 737: {INTLIB}, A Portable {FORTRAN 77} Interval Standard Function Library},
   JOURNAL = {ACM Trans.\ Math.\ Software},
   VOLUME = "20",
   NUMBER ="4",
   PAGES ="447--459",
   MONTH ="December",
   YEAR = "1994"
}
@INPROCEEDINGS{princeton-opt,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Test Results for an Interval Branch and Bound Algorithm for Equality-Constrained Optimization},
   PAGES ="181--200",
   PUBLISHER ="Kluwer",
   BOOKTITLE = {State of the Art in Global Optimization: Computational Methods and Applications},
   EDITOR ={C. Floudas and P. M. Pardalos},
   ADDRESS ="Dordrecht, Netherlands",
   YEAR = "1995"
}
@MISC{computing-non-smoo,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Interval Extensions of Non-Smooth Functions for Global Optimization and Nonlinear Systems Solvers},
NOTE={Accepted for publication in {\it Computing}},
   YEAR = "1995"
}
@ARTICLE{f90mods,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {A {Fortran 90} Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization},
   JOURNAL = {ACM Trans.\ Math.\ Software},
   VOLUME = "21",
   NUMBER ="1",
   PAGES ="63--78",
   MONTH ="March",
   YEAR = "1995"
}
@INPROCEEDINGS{wuppertal-non-smoo,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Treating Non-Smooth Functions as Smooth Functions in Global Optimization and Nonlinear Systems Solvers},
   PUBLISHER ="Akademie Verlag",
   BOOKTITLE = {Scientific Computing and Validated Numerics},
   EDITOR ={G. Alefeld and A. Frommer},
   SERIES ="Mathematical Research",
   ADDRESS ="Berlin",
   YEAR = "1995"
}
@BOOK{opt-book,
   AUTHOR = {Kearfott, R. B.},
   TITLE = {Rigorous Global Search: Continuous Problems},
   PUBLISHER ="Kluwer",
   ADDRESS ="Dordrecht, Netherlands",
   YEAR = "1996"
}
@INPROCEEDINGS{shi-scan95,
   AUTHOR = {Kearfott, R. B. and Shi, X.},
   TITLE = {Optimal Preconditioners for the Interval Gauss--Seidel Method},
   PUBLISHER ="Akademie Verlag",
   BOOKTITLE = {Scientific Computing and Validated Numerics},
   EDITOR ={G. Alefeld and A. Frommer},
   SERIES ="Mathematical Research",
   ADDRESS ="Berlin",
   YEAR = "1996"
}
@ARTICLE{kedem,
   AUTHOR = {Kedem, G.},
   TITLE = {Automatic Differentiation of Computer Programs},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "6",
   NUMBER ="2",
   PAGES ="150--165",
   YEAR = "1980"
}
@ARTICLE{keiper-intarith,
   AUTHOR = {Keiper, J. B.},
   TITLE = {Interval Arithmetic in {Mathematica}},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="3",
   PAGES ="76--87",
   YEAR = "1993"
}
@BOOK{c-xsc-book,
   AUTHOR = {Klatte, R. and Kulisch, U. and Wiethoff, A. and Lawo, C. and Rauch, M.},
   TITLE = {{C-XSC  A C++} Class Library for Extended Scientific Computing},
   PUBLISHER ="Springer-Verlag",
   ADDRESS ="New York",
   YEAR = "1993"
}
@ARTICLE{bias-computing,
   AUTHOR = {{Kn\"uppel}, O.},
   TITLE = {{PROFIL/BIAS --- A} Fast Interval Library},
   JOURNAL = {Computing},
   VOLUME = "53",
   PAGES ="277--287",
   YEAR = "1994"
}
@INPROCEEDINGS{esprit-ada,
   AUTHOR = {Kok, J.},
   TITLE = {The Embedding of Accurate Arithmetic in {Ada}},
   PAGES ="99--120",
   PUBLISHER ="Wiley",
   BOOKTITLE = {Improving Floating Point Programming},
   EDITOR ={Wallis, P. J. L.},
   ADDRESS ="New York",
   YEAR = "1990"
}
@INPROCEEDINGS{modula-sc,
   AUTHOR = {Falco-Korn, C. and Gutzwiller, S. and {K\"unig}, S. and Ullrich, Ch.},
   TITLE = {{Modula-SC}, Motivation, Language Definition and Implementation},
   PAGES ="161--180",
   PUBLISHER ="J. C. Baltzer AG",
   BOOKTITLE = {Computer Arithmetic -- Scientific Computation and Mathematical Modelling},
   EDITOR ={Kaucher, E. and Markov, S. and Mayer, G.},
   SERIES ="{IMACS} Annals on Computing and Applied Math. 12",
   ADDRESS ="Basel",
   YEAR = "1992"
}
@MISC{korn-extending-linpack,
   AUTHOR = {C. F. Korn and Ch. Ullrich},
   TITLE = {Extending {LINPACK} by Verification Routines for Linear Systems},
NOTE={Talk given at IMACS / GAMM International Symposium (SCAN-93), Vienna, Austria, 09/26/1993 -- 09/29/1993},
   YEAR = "1993"
}
@PHDTHESIS{kraemer-diss,
   AUTHOR = {{Kr\"amer}, W.},
   TITLE = {{Inverse Standardfunktionen {f\"ur} reelle und komplexe Intervallargumente mit a priori {Fehlerabsch\"atzungen}}},
   SCHOOL ={{Universit\"at Karlsruhe}},
   YEAR = "1987"
}
@INPROCEEDINGS{kramer-multiple-precision,
   AUTHOR = {Kr{\"a}mer, W.},
   TITLE = {Multiple Precision Computations with Result Verification},
   PAGES ="325--256",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Scientific Computing with Automatic Result Verification},
   EDITOR ={E. Adams and U. Kulisch},
   SERIES ="Mathematics in Science and Engineering, volume 189",
   ADDRESS ="New York",
   YEAR = "1993"
}
@ARTICLE{krawczyk-method,
   AUTHOR = {Krawczyk, R.},
   TITLE = {{Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlershranken}},
   JOURNAL = {Computing},
   VOLUME = "4",
   PAGES ="187--201",
   YEAR = "1969"
}
@ARTICLE{krawczyk-nickel,
   AUTHOR = {Krawczyk, R. and  Nickel, K.},
   TITLE = {The Centered Form in Interval Arithmetics: Quadratic Convergence and Inclusion Isotonicity},
   JOURNAL = {Computing},
   VOLUME = "28",
   NUMBER ="2",
   PAGES ="117--137",
   YEAR = "1982"
}
@ARTICLE{krawczyk-neumaier-slopes,
   AUTHOR = {Krawczyk, R. and Neumaier, A.},
   TITLE = {Interval Slopes for Rational Functions and Associated Centered Forms},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "22",
   NUMBER ="3",
   PAGES ="604--616",
   MONTH ="June",
   PUBLISHER ="SIAM",
   YEAR = "1985"
}
@ARTICLE{krishchuk-f77-preprocessor,
   AUTHOR = {Krishchuk, V. N. and Vasilega, N. M. and Kozina, G. L.},
   TITLE = {Interval Operations and Functions Library for {FORTRAN 77} Programming System and its Practice Using},
   JOURNAL = {Interval Computations},
   VOLUME = "4",
   NUMBER ="6",
   PAGES ="2--8",
   YEAR = "1992"
}
@ARTICLE{kristinsdottir,
   AUTHOR = {Kristinsdottir, B. P. and Zabinsky, Z. B. and Csendes, T. and Tuttle, M. E.},
   TITLE = {Methodologies for Tolerance Intervals},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="3",
   PAGES ="133--147",
   YEAR = "1993"
}
@INPROCEEDINGS{kulisch-new-arithmetic,
   AUTHOR = {Kulisch, U. W.},
   TITLE = {A New Arithmetic for Scientific Computation},
   PAGES ="1--26",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {A New Approach to Scientific Computation},
   EDITOR ={Kulisch, U. W. and Miranker, W. L.},
   SERIES ="Notes and Repors in Comp. Sci. and Applied Math.",
   ADDRESS ="New York",
   YEAR = "1983"
}
@PROCEEDINGS{kulisch-miranker,

   TITLE = {A New Approach to Scientific Computation},
   PUBLISHER ="Academic Press",
   EDITOR ={Kulisch, U. W. and Miranker, W. L.},
   ADDRESS ="New York",
   YEAR = "1983"
}
@ARTICLE{kulisch-siam-rev,
   AUTHOR = {Kulisch, U. W. and  Miranker, W. L.},
   TITLE = {The Arithmetic of the Digital Computer: A New Approach},
   JOURNAL = {SIAM Rev.},
   VOLUME = "28",
   NUMBER ="1",
   PAGES ="1--40",
   YEAR = "1986"
}
@ARTICLE{kuprianova,
   AUTHOR = {Kupriyanova, L.},
   TITLE = {Inner Estimation of the United Solution Set of Interval Algebraic Systems},
   JOURNAL = {Reliable Computing},
   VOLUME = "1",
   PAGES ="15--32",
   YEAR = "1995"
}
@INPROCEEDINGS{laveuve-kahan-arithmetic,
   AUTHOR = {Laveuve, S. E.},
   TITLE = {{Definition einer Kahan-Arithmetik und ihre Implementierung}},
   PAGES ="236--245",
   PUBLISHER ="Springer-Verlag",
   BOOKTITLE = {Interval Mathematics},
   EDITOR ={K. Nickel},
   SERIES ="Lecture Notes in Computer Science 25",
   ADDRESS ="New York",
   YEAR = "1975"
}
@INPROCEEDINGS{c-xsc,
   AUTHOR = {Lawo, C.},
   TITLE = {{C-XSC} -- A Programming Environment for Verified Scientific Computing and Numerical Data Processing},
   PAGES ="71--86",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Scientific Computing with Automatic Result Verification},
   EDITOR ={Adams, E. and Kulisch, U.},
   ADDRESS ="New York, etc.",
   YEAR = "1993"
}
@ARTICLE{blas-toms-algorithm,
   AUTHOR = {Lawson, C. L. and Hanson, R. J. and Kincaid, D. R. and Krogh, F. T.},
   TITLE = {Algorithm 539 Basic Linear Algebra Subprograms for {FORTRAN} Usage},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "5",
   NUMBER ="3",
   PAGES ="308--325",
   MONTH ="September",
   YEAR = "1979"
}
@ARTICLE{leclerc-ic-parallel,
   AUTHOR = {Leclerc, A.},
   TITLE = {Parallel Interval Global Optimization in {C++}},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="3",
   PAGES ="148--163",
   YEAR = "1993"
}
@BOOK{lloyd-degree-theory-book,
   AUTHOR = {Lloyd, N. G.},
   TITLE = {Degree Theory},
   PUBLISHER ="Cambridge University Press",
   ADDRESS ="Cambridge, England",
   YEAR = "1978"
}
@ARTICLE{lodwick-constraints,
   AUTHOR = {Lodwick, W. A.},
   TITLE = {Constraint Propagation, Relational Arithmetic in AI Systems and Mathematical Programs},
   JOURNAL = {Ann. Oper. Res.},
   VOLUME = "21",
   NUMBER ="1-4",
   PAGES ="143--148",
   YEAR = "1989"
}
@TECHREPORT{luther-otten-standard-fns,
   AUTHOR = {Luther, W. and Otten, W.},
   TITLE = {Computation of Standard Interval Functions in Multiple-Precision Interval Arithmetic},
   INSTITUTION ="Uni. Duisburg Gesamthochschule",
   NUMBER ="SM-DU-233",
   YEAR = "1993"
}
@ARTICLE{markov-first-extended,
   AUTHOR = {Markov, S. M.},
   TITLE = {Some Applications of Extended Interval Arithmetic to Interval Iterations},
   JOURNAL = {Computing (Suppl.)},
   VOLUME = "2",
   PAGES ="69--84",
   YEAR = "1980"
}
@INPROCEEDINGS{markov-michigan,
   AUTHOR = {Markov, S.},
   TITLE = {On an Interval Arithmetic and its Applications},
   BOOKTITLE = {Proceedings of the 5th Symposium on Computer Arithmetic. IEEE. Univ. Michigan. 1981. Ann Arbor, MI, USA. 18-19 May 1981.},
   YEAR = "1981"
}
@MISC{mayer-epsilon-inflation,
   AUTHOR = {Mayer, G.},
   TITLE = {Epsilon--Inflation in Verification Algorithms},
NOTE={Preprint, Fachbereich Mathematik, Universit{\"a}t Rostock, Postfach 6980, D-18051 Rostock, GERMANY},
   YEAR = "1993"
}
@INPROCEEDINGS{ohio-fsc-metzger,
   AUTHOR = {Metzger, M.},
   TITLE = {{FORTRAN-SC}, A {FORTRAN} Extension for Engineering / Scientific Computation with Access to {ACRITH}:  Demonstration},
   PAGES ="63--80",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Reliability in Computing},
   EDITOR ={Moore, R. E.},
   SERIES ="Perspectives in Computing",
   ADDRESS ="New York",
   YEAR = "1988"
}
@BOOK{m77,
   AUTHOR = {{University of Minnesota Computer Center}},
   TITLE = {M77 Reference Manual:  1977 Standards Version Edition 1},
   PUBLISHER ="University of Minnesota",
   YEAR = "1983"
}
@ARTICLE{miranda,
   AUTHOR = {Miranda, C.},
   TITLE = {Un' Osservatione su un Teorema di Brower},
   JOURNAL = {Bol. Un. Mat. Ital., Series 2},
   VOLUME = "2",
   PAGES ="5--7",
   YEAR = "1940"
}
@INPROCEEDINGS{mladenov-problems,
   AUTHOR = {Mladenov, V.},
   TITLE = {An Improved Interval Method for Solving Nonlinear Systems of Monotone Functions},
   PAGES ="23--26",
   PUBLISHER ="DATECS Publishing",
   BOOKTITLE = {Mathematical Modelling and Scientific Computing},
   EDITOR ={S. M. Markov},
   ADDRESS ="Sofia",
   YEAR = "1993"
}
@PHDTHESIS{moore-dissertation,
   AUTHOR = {Moore, R. E.},
   TITLE = {Interval Arithmetic and Automatic Error Analysis in Digital Computing},
   MONTH ="October",
   PUBLISHER ="UMI",
   SCHOOL ={{Stanford University}},
   YEAR = "1962"
}
@ARTICLE{moore-siam-existence-test,
   AUTHOR = {Moore, R. E.},
   TITLE = {A Test for Existence of Solutions to Nonlinear Systems},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "14",
   NUMBER ="4",
   PAGES ="611--615",
   MONTH ="September",
   YEAR = "1977"
}
@ARTICLE{moore-jones-safe-regions,
   AUTHOR = {Moore, R. E. and Jones, S. T.},
   TITLE = {Safe Starting Regions for Iterative Methods},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "14",
   NUMBER ="6",
   PAGES ="1051--1065",
   MONTH ="December",
   YEAR = "1977"
}
@BOOK{moore-book,
   AUTHOR = {Moore, R. E.},
   TITLE = {Methods and Applications of Interval Analysis},
   PUBLISHER ="SIAM",
   ADDRESS ="Philadelphia",
   YEAR = "1979"
}
@ARTICLE{moore-ratschek-inclusion-functions,
   AUTHOR = {Moore, R. E. and Ratschek, H.},
   TITLE = {Inclusion Functions and Global Optimization {II}},
   JOURNAL = {Math. Prog.},
   VOLUME = "41",
   NUMBER ="3",
   PAGES ="341--356",
   MONTH ="September",
   YEAR = "1988"
}
@INPROCEEDINGS{moore-hansen-leclerc,
   AUTHOR = {Moore, R. E. and Hansen, E. and Leclerc, A.},
   TITLE = {Rigorous Methods for Parallel Global Optimization},
   PAGES ="321--342",
   PUBLISHER ="Princeton Univ. Press",
   BOOKTITLE = {Recent Advances in Global Optimization},
   EDITOR ={A. Floudas and P. Pardalos},
   ADDRESS ="Princeton, N.J.",
   YEAR = "1992"
}
@BOOK{more-wright-software-guide,
   AUTHOR = {{Mor\'e}, J. J. and Wright, S. J.},
   TITLE = {Optimization Software Guide},
   PUBLISHER ="SIAM",
   SERIES ="Frontiers in Applied Mathematics 14",
   ADDRESS ="Philadelphia",
   YEAR = "1993"
}
@TECHREPORT{minpack-guide,
   AUTHOR = {{Mor\'e}, J. J. and Garbow, B. S. and Hillstrom, K. E.},
   TITLE = {User Guide {for MINPACK-1}},
   INSTITUTION ="Argonne National Laboratories",
   NUMBER ="ANL-80-74",
   YEAR = "1980"
}
@ARTICLE{morgan-1983-acm-tests,
   AUTHOR = {Morgan, A. P.},
   TITLE = {A Method for Computing all Solutions to Systems of Polynomial Equations},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "9",
   NUMBER ="1",
   PAGES ="1--17",
   YEAR = "1983"
}
@ARTICLE{morgan-sommese-continuation,
   AUTHOR = {Morgan, A. P. and  Sommese, A. J.},
   TITLE = {Computing all Solutions to Polynomial Systems using Homotopy Continuation},
   JOURNAL = {Appl. Math. Comput.},
   VOLUME = "24",
   NUMBER ="2",
   PAGES ="115--138",
   YEAR = "1987"
}
@ARTICLE{mudur-koparkar-geometry-review,
   AUTHOR = {Mudur, S. P. and Koparkar, P. A.},
   TITLE = {Interval Methods for Processing Geometric Objects},
   JOURNAL = {IEEE Comput. Graphics and Appl.},
   VOLUME = "4",
   NUMBER ="2",
   PAGES ="7--17",
   MONTH ="February",
   YEAR = "1984"
}
@TECHREPORT{minos-user-guide,
   AUTHOR = {Murtagh, B. A. and Saunders, M. A.},
   TITLE = {MINOS 5.1 User's Guide},
   INSTITUTION ="Dept. Operations Res., Stanford University",
   NUMBER ="SOL 83-20R",
   YEAR = "1987"
}
@BOOK{neumaier-book,
   AUTHOR = {Neumaier, A.},
   TITLE = {Interval Methods for Systems of Equations},
   PUBLISHER ="Cambridge University Press",
   ADDRESS ="Cambridge, England",
   YEAR = "1990"
}
@ARTICLE{neumaier-shen-kantorovich,
   AUTHOR = {Neumaier, A. and Z. Shen},
   TITLE = {The {Krawczyk} Operator and {Kantorovich's} Theorem},
   JOURNAL = {Mathematical Analysis and Applications},
   VOLUME = "149",
   NUMBER ="2",
   PAGES ="437--443",
   MONTH ="July",
   YEAR = "1990"
}
@MISC{neumaier-input-format,
   AUTHOR = {Neumaier, A.},
   TITLE = {A Compact Input Format for Nonlinear Optimization Problems},
NOTE={Preprint, Institut {f\"ur} Mathematik, Universit{\"a}t Wien, Strudhofgasse 4, A-1050 Wien, AUSTRIA},
   YEAR = "1993"
}
@MISC{neumaier-second-order-sufficient,
   AUTHOR = {Neumaier, A.},
   TITLE = {Second-Order Sufficient Optimality Conditions for Local and Global Nonlinear Programming},
NOTE={Preprint, Institut {f\"ur} Mathematik, Universit{\"a}t Wien, Strudhofgasse 4, A-1050 Wien, AUSTRIA},
   YEAR = "1994"
}
@TECHREPORT{ning-higher-order,
   AUTHOR = {Ning, S.},
   TITLE = {A Report on Code Lists for Higher-Order Derivatives Summary of a Fall, 1993 Individual Study Course},
   INSTITUTION ="Univ. of Southwestern La., University of Southwestern Louisiana",
   NUMBER ="{Dept.\ Math.}",
   YEAR = "1993"
}
@MISC{novoa-unpublished,
   AUTHOR = {Novoa, {Manuel III}},
   TITLE = {Theory of Preconditioners for the Interval Gauss--Seidel Method and Existence / Uniqueness Theory with Interval Newton Methods},
NOTE={Preprint, Department of Mathematics, University of Southwestern Louisiana, U.S.L. Box 4-1010, Lafayette, LA 70504},
   YEAR = "1993"
}
@ARTICLE{oettli,
   AUTHOR = {Oettli, W.},
   TITLE = {On the Solution Set of a Linear System with Inaccurate Coefficients},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "2",
   PAGES ="115--118",
   YEAR = "1965"
}
@BOOK{pardalos-rosen-constrained,
   AUTHOR = {Pardalos, P. M. and Rosen, J. B.},
   TITLE = {Constrained Global Optimization:  Algorithms and Applications},
   PUBLISHER ="Springer-Verlag",
   SERIES ="Lecture Notes in Computer Science no. 268",
   ADDRESS ="New York",
   YEAR = "1987"
}
@ARTICLE{pardalos-qp-nphard,
   AUTHOR = {Pardalos, P. M. and Vavasis, S. A.},
   TITLE = {Quadratic Programming with One Negative Eigenvalue is {NP}-Hard},
   JOURNAL = {Journal of Global Optimization},
   VOLUME = "1",
   NUMBER ="1",
   PAGES ="15--22",
   YEAR = "1992"
}
@BOOK{peterson-object-oriented-book,
   AUTHOR = {Peterson, G.},
   TITLE = {Object-Oriented Computing, Volume 1: Concepts},
   PUBLISHER ="IEEE Computer Society Press",
   ADDRESS ="Washington, D.C.",
   YEAR = "1987"
}
@TECHREPORT{c-bias,
   AUTHOR = {Qiao, L.},
   TITLE = {Basic Interval Arithmetic Subroutines Library in the {C} Language},
   MONTH ="November",
   INSTITUTION ="Math./Stat./Comp. Sci., Marquette University",
   NUMBER ="335",
   YEAR = "1990"
}
@ARTICLE{rall-kantorovich,
   AUTHOR = {Rall, L. B.},
   TITLE = {A Comparison of the Existence Theorems of {Kantorovich} and {Moore}},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "17",
   NUMBER ="1",
   PAGES ="148--161",
   YEAR = "1980"
}
@BOOK{rall-book,
   AUTHOR = {Rall, L. B.},
   TITLE = {Automatic Differentiation: Techniques and Applications},
   PUBLISHER ="Springer",
   SERIES ="Lecture Notes in Computer Science no. 120",
   ADDRESS ="Berlin, New York, etc.",
   YEAR = "1981"
}
@ARTICLE{pascal-sc,
   AUTHOR = {Rall, L. B.},
   TITLE = {An Introduction to the Scientific Computing Language {Pascal-SC}},
   JOURNAL = {Computers and Mathematics with Applications},
   VOLUME = "14",
   NUMBER ="1",
   PAGES ="53--59",
   YEAR = "1987"
}
@BOOK{ratschek-rokne-range,
   AUTHOR = {Ratschek, H. and Rokne, J.},
   TITLE = {Computer Methods for the Range of Functions},
   PUBLISHER ="Horwood",
   ADDRESS ="Chichester, England",
   YEAR = "1984"
}
@BOOK{ratschek-rokne-optimization,
   AUTHOR = {Ratschek, H. and Rokne, J.},
   TITLE = {New Computer Methods for Global Optimization},
   PUBLISHER ="Wiley",
   ADDRESS ="New York",
   YEAR = "1988"
}
@ARTICLE{ratschek-unbounded-domains,
   AUTHOR = {Ratschek, H. and  Voller, R. L.},
   TITLE = {Global Optimization over Unbounded Domains},
   JOURNAL = {SIAM J. Control Optim.},
   VOLUME = "28",
   NUMBER ="3",
   PAGES ="528--539",
   YEAR = "1990"
}
@ARTICLE{ratrok-widths,
   AUTHOR = {Ratschek, H. and Rokne, J.},
   TITLE = {Formulas for the Width of Interval Products},
   JOURNAL = {Reliable Computing},
   VOLUME = "1",
   NUMBER ="1",
   PAGES ="9--14",
   YEAR = "1995"
}
@PHDTHESIS{ratz-dissertation,
   AUTHOR = {Ratz, D.},
   TITLE = {{Automatische Ergebnisverifikation bei globalen Optimierungsproblemen}},
   SCHOOL ={{Universit\"at Karlsruhe}},
   YEAR = "1992"
}
@INPROCEEDINGS{ratz-scan91,
   AUTHOR = {Ratz, D.},
   TITLE = {An Inclusion Algorithm for Global Optimization in a Portable {PASCAL-XSC} Implementation},
   PAGES ="329--338",
   PUBLISHER ="North-Holland",
   BOOKTITLE = {Computer Arithmetic and Enclosure Methods},
   EDITOR ={Atanassova, L. and Herzberger, J.},
   ADDRESS ="Amsterdam, Netherlands",
   YEAR = "1992"
}
@ARTICLE{ratz-box-splitting,
   AUTHOR = {Ratz, D.},
   TITLE = {Box-Splitting Strategies for the Interval {Gauss--Seidel} Step in a Global Optimization Method},
   JOURNAL = {Computing},
   VOLUME = "53",
   PAGES ="337--354",
   YEAR = "1994"
}
@INPROCEEDINGS{ratz-scan,
   AUTHOR = {Ratz, D.},
   TITLE = {On Branching Rules in Second-Order Branch-and-Bound Methods for Global Optimization},
   PUBLISHER ="Akademie Verlag",
   BOOKTITLE = {Scientific Computing and Validated Numerics},
   EDITOR ={G. Alefeld and A. Frommer},
   SERIES ="Mathematical Research",
   ADDRESS ="Berlin",
   YEAR = "1996"
}
@BOOK{rheinboldt-ortega,
   AUTHOR = {Rheinboldt, W. C. and Ortega, J. M.},
   TITLE = {Iterative Solution of Nonlinear Equations in Several Variables},
   PUBLISHER ="Academic Press",
   ADDRESS ="New York",
   YEAR = "1970"
}
@INPROCEEDINGS{rohn-ohio,
   AUTHOR = {Rohn, J.},
   TITLE = {Solving Systems of Linear Interval Equations},
   PAGES ="171--182",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Reliability in Computing},
   EDITOR ={R. E. Moore},
   SERIES ="Perspectives in Computing",
   ADDRESS ="New York",
   YEAR = "1988"
}
@ARTICLE{rohn-condition-numbers,
   AUTHOR = {Rohn, J.},
   TITLE = {New Condition Numbers for Matrices and Linear Systems},
   JOURNAL = {Computing},
   VOLUME = "41",
   NUMBER ="1--2",
   PAGES ="167--169",
   YEAR = "1989"
}
@MISC{rohn-nphard,
   AUTHOR = {Rohn, J.},
   TITLE = {{NP}-Hardness Results for Linear Algebraic Problems with Interval Data},
NOTE={Preprint, Faculty of Math. and Physics, Charles University, Malostranske nam. 25, 11800 Praha 1, CZECH REPUBLIC},
   YEAR = "1994"
}
@ARTICLE{rohn-hull-np-hard,
   AUTHOR = {Rohn, J. and Kreinovich, V.},
   TITLE = {Computing Exact Componentwise Bounds on Solutions of Linear Systems with Interval Data is {NP}-Hard},
   JOURNAL = {SIAM J. Matrix Anal. Appl.},
   VOLUME = "16",
   NUMBER ="2",
   MONTH ="April",
   YEAR = "1995"
}
@PHDTHESIS{rump-diss,
   AUTHOR = {Rump, S. M.},
   TITLE = {{Kleine Fehlerschranken bei Matrixproblemen}},
   SCHOOL ={{Universit\"at Karlsruhe}},
   YEAR = "1980"
}
@INPROCEEDINGS{rump-acrith,
   AUTHOR = {Rump, S. M.},
   TITLE = {{ACRITH} -- High Accuracy Arithmetic Subroutine Library},
   PUBLISHER ="Springer-Verlag",
   BOOKTITLE = {EUROCAL '85: European Conference on Computer Algebra},
   EDITOR ={Buchberger, B.},
   ADDRESS ="New York",
   YEAR = "1985"
}
@ARTICLE{rump-slope,
   AUTHOR = {Rump, S. M.},
   TITLE = {On the Solution of Interval Linear Systems},
   JOURNAL = {Computing},
   VOLUME = "47",
   PAGES ="337--353",
   YEAR = "1992"
}
@INPROCEEDINGS{rump-survey,
   AUTHOR = {Rump, S. M.},
   TITLE = {Verification Methods for Dense and Sparse Systems of Equations},
   PAGES ="63--135",
   PUBLISHER ="Elsevier Science Publishers",
   BOOKTITLE = {Topics in Validated Computations},
   EDITOR ={J. Herzberger},
   ADDRESS ="Amsterdam",
   YEAR = "1994"
}
@MISC{rump-range,
   AUTHOR = {Rump, S. M.},
   TITLE = {Expansion and Estimation of the Range of Nonlinear Functions},
NOTE={Preprint, Informatik III -- Programmiersprachen und Algorithmen, Technische Universitaet Hamburg, Eissendorfer Strasse 38, 2100 Hamburg 90, GERMANY},
   YEAR = "1995"
}
@TECHREPORT{rump-componentwise-distance,
   AUTHOR = {Rump, S. M.},
   TITLE = {Bounds for the Componentwise Distance to the Nearest Singular Matrix},
   INSTITUTION ="Technical University Hamburg-Harburg",
   NUMBER ="95.3",
   YEAR = "1995"
}
@MISC{rump-scan95,
   AUTHOR = {S. M. Rump},
   TITLE = {New Results on Validation Algorithms for Large Systems of Equations},
NOTE={Talk given at SCAN'95, Wuppertal, Germany, Sept. 26 -- 29, 1995},
   YEAR = "1995"
}
@PHDTHESIS{schnepper-diss,
   AUTHOR = {Schnepper, C. A.},
   TITLE = {Large Grained Parallelism in Equation-Based Flowsheeting Using Interval {Newton} / Generalized Bisection Techniques},
   PAGES ="369",
   SCHOOL ={{University of Illinois, Urbana}},
   YEAR = "1992"
}
@ARTICLE{schnepper-ic,
   AUTHOR = {Schnepper, C. A. and Stadtherr, M. A.},
   TITLE = {Application of a Parallel Interval {Newton} / Generalized Bisection Algorithm to Equation-Based Chemical Process Flowsheeting},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="4",
   PAGES ="40--64",
   YEAR = "1993"
}
@ARTICLE{sederberg-comparisons,
   AUTHOR = {Sederberg, T. W. and Parry, S. R.},
   TITLE = {Comparison of Three Curve Intersection Algorithms},
   JOURNAL = {Comput. Aided Des.},
   VOLUME = "18",
   NUMBER ="1",
   PAGES ="58--63",
   YEAR = "1986"
}
@ARTICLE{shary-algebraic-approach,
   AUTHOR = {Shary, S.},
   TITLE = {Algebraic Approach to the Interval Linear Static Identification, Tolerance and Control Problems},
   JOURNAL = {Interval Computations},
   YEAR = "1994"
}
@ARTICLE{shary-tolerance,
   AUTHOR = {Shary, S. P.},
   TITLE = {Solving the Tolerance Problem for Interval Linear Systems},
   JOURNAL = {Interval Computations},
   VOLUME = "1994",
   NUMBER ="2",
   YEAR = "1994"
}
@ARTICLE{shary-hull-computation,
   AUTHOR = {Shary, S. P.},
   TITLE = {On Optimal Solution of Interval Linear Equations},
   JOURNAL = {SIAM J. Numer. Anal.},
   VOLUME = "32",
   NUMBER ="2",
   PAGES ="610--630",
   MONTH ="April",
   YEAR = "1995"
}
@TECHREPORT{shen-wolfe-slope,
   AUTHOR = {Shen, Z. and Wolfe, M. A.},
   TITLE = {On Interval Enclosures Using Slope Arithmetic},
   MONTH ="September",
   INSTITUTION ="Dept. Math., Univ. of St. Andrews, North Haugh,",
   YEAR = "1989"
}
@ARTICLE{shen-minimax,
   AUTHOR = {Z. Shen and Neumaier, A. and Eiermann, M. C.},
   TITLE = {Solving Minimax Problems by Interval Methods},
   JOURNAL = {BIT},
   VOLUME = "30",
   PAGES ="742--751",
   YEAR = "1990"
}
@ARTICLE{shen-kantorovich,
   AUTHOR = {Z. Shen and Wolfe, M. A.},
   TITLE = {A Note on the Comparison of the {Kantorovich} and {Moore} Theorems},
   JOURNAL = {Nonlinear Analysis},
   VOLUME = "15",
   NUMBER ="3",
   PAGES ="229--232",
   YEAR = "1990"
}
@ARTICLE{sherbrooke-cagd-nonlinear,
   AUTHOR = {Sherbrooke, E. C. and Patrikalakis, N. M.},
   TITLE = {Computation of the Solutions of Nonlinear Polynomial Systems},
   JOURNAL = {Computer Aided Geometric Design},
   VOLUME = "10",
   PAGES ="379--405",
   YEAR = "1993"
}
@PHDTHESIS{shi-diss,
   AUTHOR = {Shi, X.},
   TITLE = {Intermediate Expression Preconditioning and Verification for Rigorous Solution of Nonlinear Systems},
   MONTH ="August",
   SCHOOL ={{University of Southwestern Louisiana}},
   ADDRESS ="Department of Mathematics",
   YEAR = "1995"
}
@PHDTHESIS{shiriaev-vector,
   AUTHOR = {Shiriaev, D.},
   TITLE = {Fast Automatic Differentiation for Vector Processors and Reduction of the Spatial Complexity in a Source Translation Environment},
   SCHOOL ={{University of Karlsruhe}},
   YEAR = "1993"
}
@ARTICLE{skelboe-algorithm,
   AUTHOR = {Skelboe, S.},
   TITLE = {Computation of Rational Interval Functions},
   JOURNAL = {BIT},
   VOLUME = "14",
   PAGES ="87--95",
   YEAR = "1974"
}
@TECHREPORT{speelpenning,
   AUTHOR = {Speelpenning, B.},
   TITLE = {Compiling Fast Partial Derivatives of Functions Given by Algorithms},
   MONTH ="January",
   INSTITUTION ="Univ. of Illinois at Urbana--Chambaign",
   NUMBER ="R-80-1002",
   YEAR = "1980"
}
@BOOK{maple-book,
   AUTHOR = {{Symbolic Computation Group Staff}},
   TITLE = {Maple, Version 4.2.1},
   PUBLISHER ="Brooks/Cole",
   ADDRESS ="Monterey, California",
   YEAR = "1990"
}
@ARTICLE{stenger-degree,
   AUTHOR = {Stenger, F.},
   TITLE = {An Algorithm for the Topological Degree of a Mapping in {$\R{n}$}},
   JOURNAL = {Numer. Math.},
   VOLUME = "25",
   PAGES ="23--38",
   PUBLISHER ="Springer",
   YEAR = "1976"
}
@TECHREPORT{IEEE-binary-standard,
   AUTHOR = {{Stevenson, D., chairman, Floating-Point Working Group, Microprocessor Standards Subcommittee}},
   TITLE = {{IEEE} Standard for Binary  Floating Point Arithmetic {(IEEE/ANSI 754-1985)}},
   PUBLISHER ="IEEE",
   INSTITUTION ="IEEE",
   YEAR = "1985"
}
@PHDTHESIS{stynes-dissertation,
   AUTHOR = {Stynes, M.},
   TITLE = {An Algorithm for the Numerical Calculation of the Degree of a Mapping},
   SCHOOL ={{Oregon State University}},
   ADDRESS ="Department of Mathematics, Corvallis, Oregon",
   YEAR = "1977"
}
@BOOK{van-hentenryck-book,
   AUTHOR = {Van Hentenryck, P.},
   TITLE = {Constraint Satisfaction in Logic Programming},
   PUBLISHER ="MIT Press",
   ADDRESS ="Cambridge, MA",
   YEAR = "1989"
}
@TECHREPORT{van-hentenryck,
   AUTHOR = {{Van Hentenryck}, P. and McAllester, D. and Kapur, D.},
   TITLE = {Solving Polynomial Systems Using a Branch and Prune Approach},
   INSTITUTION ="Dept. of Comp. Sci., Brown University",
   NUMBER ="CS-95-01",
   YEAR = "1995"
}
@ARTICLE{vrahatis-degree,
   AUTHOR = {Vrahatis, M. N.},
   TITLE = {Solving Systems of Nonlinear Equations Using the Nonzero Value of the Topological Degree},
   JOURNAL = {ACM Trans. Math. Software},
   VOLUME = "14",
   NUMBER ="4",
   PAGES =" 312--336",
   MONTH ="December",
   YEAR = "1988"
}
@INPROCEEDINGS{walster-hansen-test-results,
   AUTHOR = {Walster, G. W. and Hansen, E. R. and Sengupta, S.},
   TITLE = {Test Results for a Global Optimization Algorithm},
   PAGES ="272--287",
   PUBLISHER ="SIAM",
   BOOKTITLE = {Numerical Optimization 1984},
   EDITOR ={P. T. Boggs and R. H. Byrd and R. B. Schnabel},
   ADDRESS ="Philadelphia",
   YEAR = "1985"
}
@INPROCEEDINGS{ohio-fsc-walter,
   AUTHOR = {Walter, W. V.},
   TITLE = {{FORTRAN-SC}, a Fortran Extension for Engineering / Scientific Computation with Access to {ACRITH}:  Language Description},
   PAGES ="43--62",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Reliability in Computing},
   EDITOR ={R. E. Moore},
   SERIES ="Perspectives in Computing",
   ADDRESS ="New York",
   YEAR = "1988"
}
@ARTICLE{fortran-xsc,
   AUTHOR = {Walter, W. V.},
   TITLE = {{FORTRAN-XSC:  A} Portable {Fortran 90} Module Library for Accurate and Reliable Scientific Computing},
   JOURNAL = {Computing (Suppl.)},
   VOLUME = "9",
   PAGES ="265--286",
   YEAR = "1993"
}
@INPROCEEDINGS{acrith-xsc,
   AUTHOR = {Walter, W. V.},
   TITLE = {{ACRITH-XSC: A} {Fortran}-Like Language for Verified Scientific Computing},
   PAGES ="45--70",
   PUBLISHER ="Academic Press",
   BOOKTITLE = {Scientific Computing with Automatic Result Verification},
   EDITOR ={Adams, E. and  Kulisch, U.},
   ADDRESS ="New York, etc.",
   YEAR = "1993"
}
@ARTICLE{wengert-autodiff,
   AUTHOR = {Wengert, R. E.},
   TITLE = {A simple Automatic Derivative Evaluation Program},
   JOURNAL = {Comm. ACM},
   VOLUME = "7",
   NUMBER ="8",
   PAGES ="463--464",
   MONTH ="August",
   YEAR = "1964"
}
@ARTICLE{wexler,
   AUTHOR = {Wexler, A. S.},
   TITLE = {Automatic Evaluation of Derivatives},
   JOURNAL = {Appl. Math. Comput.},
   VOLUME = "24",
   PAGES ="  19--26",
   YEAR = "1987"
}
@ARTICLE{wolfe-constrained,
   AUTHOR = {Wolfe, M. A.},
   TITLE = {An Interval Algorithm for Constrained Global Optimization},
   JOURNAL = {J. Comput. Appl. Math.},
   VOLUME = "50",
   PAGES ="605--612",
   YEAR = "1994"
}
@ARTICLE{sc-languages,
   AUTHOR = {Wolff von Gudenberg, J.},
   TITLE = {Programming Language Support for Scientific Computation},
   JOURNAL = {Interval Computations},
   VOLUME = "1992",
   NUMBER ="4",
   PAGES ="116--126",
   YEAR = "1992"
}
@BOOK{mathematica-book,
   AUTHOR = {Wolfram, S.},
   TITLE = {Mathematica:  A System for Doing Mathematics by Computer (Second Edition)},
   PUBLISHER ="Addison-Wesley",
   ADDRESS ="Reading, MA",
   YEAR = "1991"
}
@PHDTHESIS{xing-diss,
   AUTHOR = {Xing, Zh.},
   TITLE = {Rigorous Step Control for Continuation},
   SCHOOL ={{University of Southwestern Louisiana}},
   YEAR = "1993"
}
@ARTICLE{yakovlev-multiaspectness,
   AUTHOR = {Yakovlev, A. G.},
   TITLE = {Multiaspectness and Localization},
   JOURNAL = {Interval Computations},
   VOLUME = "1993",
   NUMBER ="4",
   PAGES ="195--209",
   YEAR = "1993"
}
@ARTICLE{yohe-package,
   AUTHOR = {Yohe, J. M.},
   TITLE = {Software for Interval Arithmetic: A Reasonably Portable Package},
   JOURNAL = {ACM Trans.\ Math.\ Software},
   VOLUME = "5",
   NUMBER ="1",
   PAGES ="50--53",
   MONTH ="March",
   YEAR = "1979"
}