From daemon Thu Feb 29 16:47:32 1996
Received: from interval.usl.edu by homer.cma.univie.ac.at; (5.65v3.2/1.1.8.2/12Jan95-0202PM)
id AA09634; Thu, 29 Feb 1996 16:26:12 +0100
Received: by interval.usl.edu id AA06544
(5.65c/IDA-1.4.4 for neum@cma.univie.ac.at); Thu, 29 Feb 1996 09:05:04 -0600
Date: Thu, 29 Feb 1996 09:05:04 -0600
From: "Kearfott R. Baker"
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"
}