http://interval.louisiana.edu/preprints.html
Preprints
Last updated September 2, 2020, by R. B. Kearfott
/Vita
/Papers
/ PDF Scans of Older Papers / Talks / Book Reviews/Encyclopedia
of
Optimization Articles / Interval
Arithmetic
Standardization Proposal/ Acknowledgements
/
Suggestion: If you have a specific work in mind,
try using your browser's text search capabilies.
Curriculum vita, including publications that are not
available below:
- PDF file
- Send mail to rbk@louisiana.edu
for further information.
Please cite properly any of this material that you
use.
Papers
- Proceedings of the Thirteenth Annual
USL Mathematics Conference, October 22-24, 1982.
PDF
file
- A Fortran Contour Integral Package,
technical report, 1983.
PDF
file
- A Note on Homotopy Methods for
Solving Systems of Polynomial Equations Defined on the (n-1)-Sphere
and Other Manifolds, technical report, 1983.
PDF
file
- A Pivoting Scheme for the Interval
Gauss-Seidel Method: numerical experiments, joint with Chenyi
Hu, in Approximation, Optimization,
and Computing, ed. A. G. Law and C.- L. Wang, Elsevier, 1990,
pp. 97–100.
PDF
file
- Interval Mathematics Techniques for
Control Theory Computations, in Computation
and Control (proceedings from a conference held in Bozeman,
Montana, summer, 1988, pp. 169-178, Birkhäuser Boston, 1989.
PDF
file
- A Review of Preconditioners for the Interval Gauss-Seidel
Method, joint with Manuel Novoa and Chenyi Hu, Interval
Computations 1 (1), pp. 59-85 (1991).
PDF
file
Also
see a non-searchable PDF for the published version
A
related unpublished report by Manuel Novoa
- Decomposition of Arithmetic Expressions to Improve the Behavior of
Interval Iteration for Nonlinear Systems, preprint of an article
that appeared in Computing 47 (2), pp. 169-191 (1991)
PDF file
- The Cluster Problem in Global Optimization: The Univariate case,
joint with K. Du, preprint of an article that appeared in Computing
(Suppl.) 9, pp. 117-127 (1992).
PDF file
PDF
file for the figure
- INTLIB: A Portable Fortran-77
Elementary Function Library, joint with Milind Dawande,
Kaisheng Du, and Chenyi Hu, Reliable
Computing 3 (5),
pp. 96-105 (1992).
PDF
file
- An Interval Branch and Bound Algorithm for Bound Constrained
Optimization, Journal
of
Global Optimization
2, pp. 259-280 (1992).
PDF
file;
- Rigorous Computation of Surface Patch Intersection Curves,
preprint (1993).
PDF file
- A Preconditioner Selection Heuristic
for Efficient Iteration with Decomposition of Arithmetic Expressions
for Nonlinear Algebraic Systems, joint with Xiaofa Shi, Reliable
Computing 1993 (1),
pp. 15--33.
PDF
file
- On Bounding the Range of Some
Elementary Functions in FORTRAN-77, joint with Chenyi Hu,
and Abdulhamid Awad, Reliable
Computing 1993 (3),
pp.
29-40.1993(3).
PDF
file
- The Cluster Problem in Multivariate Global Optimization, joint
with K. Du, preprint of an article that appeared in the Journal
of Global Optimization 5, pp. 253-265 (1994).
PDF
file
PDF
file
for the figure
- An Interval Step Control for Continuation Methods, joint with
Z. Xing, SIAM
J. Numer. Anal. 31 (3), pp. 892-914 (1994).
PDF
file
PDF
file with a related unpublished work from 1989 with a simple algorithm
and some theory
- Algorithm 737: INTLIB: A Portable FORTRAN 77 Elementary Function
Library, ACM Trans. Math.
Software 20 (4) pp. 447-459 (December, 1994).
PDF
file
- A Fortran 90 Environment for Research and Prototyping of
Enclosure Algorithms for Constrained and Unconstrained Nonlinear
Equations, ACM Trans.
Math. Software 21 (1), pp. 251-263 (1995).
PDF
file
- A General Iterative Sparse Linear Solver and its Parallelization
for Interval Newton Methods, joint with Chenyi Hu, Anna Frolov,
and Qing Yang, Reliable
Computing 1 (3), pp. 63-78 (March, 1995).
PDF
file
- Optimizing INTBIS on the CRAY Y-MP,
joint with Chenyi Hu, Joe Sheldon, and Qing Yang, Reliable
Computing 1 (3),
pp. 265-274, (1995).
PDF
- FORTDIFF: A Set of Subroutines for Fortran-to-Fortran Differentiation
of Programs (technical report, 1995, joint with S. Ning)
PDF file
- Applications of interval Computations: An Introduction, in Applications of
Interval Computations, ed. R. B. Kearfott and V. Kreinovich,
Kluwer, Dordrecht, Netherlands, pp. 23-60, 1996.
PDF
file
- A Review of Techniques in the Verified Solution of Constrained
Global Optimization Problems, in Applications
of
Interval Computations, ed. R. B. Kearfott and V. Kreinovich,
Kluwer, Dordrecht, Netherlands, pp. 23-60, 1996.
PDF
file
- Interval Computations: Introduction, Uses, and Resources, Euromath
Bulletin 2 (1), pp. 95-112 (1996).
PDF
file
Excerpt containing
references to electronic resources (HTML)
- Automatic Differentiation of Conditional Branches in an Operator
Overloading Context, in Computational Differentiation:
Techniques, Applications, and Tools (proceedings of the Second
International Workshop on Computational Differentiation), ed. M. Berz,
C. Bischof, G. Corliss, and A. Griewank, SIAM, Philadelphia, pp. 75-81,
1996.
PDF file
- Interval Extensions of Non-Smooth Functions for Global
Optimization and Nonlinear Systems Solvers, Computing 57
(2), pp. 149-162 (1996).
PDF file
Errata
from
Corliss and Van Iwaarden
- Treating Non-Smooth Functions as Smooth Functions in Global
Optimization and Nonlinear Systems Solvers, preprint of an article
that appeared in Scientific Computing and Validated Numerics,
ed. G. Alefeld and A. Frommer, Akademie Verlag, pp. 160-172, 1996.
PDF file
- Test Results for an Interval Branch and Bound Algorithm for
Equality-Constrained Optimization, preprint of an article that
appeared in State of the Art in Global Optimization: Computational
Methods and Applications, ed. C. Floudas and P. Pardalos, Kluwer,
Dordrecht, pp. 181--200, 1996.
PDF file
- Optimal Preconditioners for Interval Gauss-Seidel Methods,
joint with S. Shi, in Scientific Computing and Validated Numerics,
ed. G. Alefeld and A. Frommer, Akademie Verlag, pp. 173-178, 1996.
PDF
file
- A Comparison of some Methods for Solving Linear Interval
Equations, joint with S. Ning, SIAM
J.
Numer. Anal. 34 (1), pp. 1289-1305 (August,
1997). Reprint from SIAM:
PDF
file
- Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 Module for an
Interval Data Type, preprint of a paper that appeared in ACM
Trans.
Math. Software 22 (4), pp. 385-392 (1996).
PDF
file
- Empirical Evaluation of Innovations in Interval Branch and Bound
Algorithms for Nonlinear Algebraic Systems, in the SIAM
Journal on Scientific Computing, 18 (2), pp. 574-594
(March, 1997); reprint from SIAM:
PDF
file
- Errata and Opinion to: "An Interval Entropy Penalty Method for
Nonlinear Global Optimization," by Zhenyu Huang, in Reliable
Computing 4 (1), pp. 89-100 (1998). (The erratum
appears in Reliable Computing 11 (2), April, 2005).
PDF
file
- On Proving Existence of Feasible Points in Equality Constrained
Optimization Problems, Mathematical Programming 83
(1), pp. 89-100 (September, 1998)
PDF file
- On Verifying Feasibility in Equality Constrained Optimization
Problems (technical report to supplement the above).
PDF
file
- Book Review of Numerica: A
Modeling Language for Global Optimization by Pascal Van
Hentenryck, Laurent Michel, and Yves Deville
- (MIT Press, Cambridge, Massachusetts, 1997), Mathematics
of Computation 49 (2), pp. 331-332 (2007).
- An Iterative Method for Finding Approximate Feasible Points,
(joint with J. Dian), technical report.
PDF
file
- Rigorous Global Search: Industrial Applications, (joint with
G. F. Corliss), in Developments in Reliable Computing, ed. T.
Csendes, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp.
1-16, 1999.
PDF file
- On Stopping Criteria in Verified Nonlinear Systems or
Optimization Algorithms (preprint of the article R. B.
Kearfott and G. W. Walster, "On Stopping Criteria in Verified Nonlinear
Systems or Optimization Algorithms," ACM
Trans. Math. Software26 (3), pp. 323-351 (September,
2000))
PDF
file
- Existence Verification for Singular Zeros of Complex Nonlinear
Systems,” SIAM
J. Numer. Anal. 38 (2), pp. 360--379 (2000). (Copyright SIAM.)
PDF
file
- Existence Verification for Singular Zeros of Complex Nonlinear
Systems, (joint with J. Dian and A. Neumaier), technical report
(expanded explanations of parts the article R. Baker Kearfott,
Jianwei Dian, and A. Neumaier, “Existence Verification for Singular
Zeros of Complex Nonlinear Systems,” SIAM
J. Numer. Anal. 38 (2), pp. 360--379 (2000). )
PDF
file
- R. B. Kearfott and A. Arazyan, Taylor Models in Deterministic
Global Optimization (joint with A. Arazyan), in Automatic
Differentiation of Algorithms: From Simulation to Optimization,
(proceedings of AD
2000, the Third International Conference and Workshop on Automatic
Differentiation, June 19-23, 2000, Nice, France), ed. G. Corliss,
Ch. Faure, A. Griewank, L. Hascoët, and U. Naumann, Springer Verlag, New
York, etc., 2002, pp. 365--372.
PDF
file
- An Example of Singularity in Nonlinear Systems, Reliable
Computing 7 (5), pp. 425--429 (2001).
PDF
file of preprint
- An Example of Singularity in Global Optimization, Reliable
Computing, technical report.
PDF
file
Verifying Topological Indices for Higher-Order Rank Deficiencies, Journal of
Complexity 18 (2), pp. 589--611 (2002). (Proceedings
of the 2000 AMS-IMS-SIAM summer research conference on Algorithms and
their Complexity for Nonlinear Problems, July 16 to July 20, 2000,
Mt. Holyoke College, edited by Christopher Sikorski)
PDF
file
- H. Muñoz and R. B. Kearfott, Slope Intervals, Generalized
Gradients, Semigradients, Slant Derivatives, and Csets, Reliable Computing
10 (3), pp. 163-193 (2004), preprint:
PDF
file
- R. B. Kearfott and J. Dian, Existence Verification for Higher
Degree Singular Zeros ofNonlinear Systems, SIAM
J.
Numer. Anal.
41 (6), pp. 2350-2373 (2003). (Copyright SIAM).
PDF file
- J. Dian and R. B. Kearfott, Existence Verification for
Singular and Nonsmooth Zeros of Real Nonlinear Systems, Math. Comp. 72
(242), pp. 757--766 (2003).
PDF file
- R. B. Kearfott and G. W. Walster, Symbolic Preconditioning with
Taylor Models: Some examples, Reliable
Computing 8 (6), pp. 453--468 (2002).
PDF
file
- H. Muñoz and R. B. Kearfott, Interval Robustness in Nonsmooth
Nonlinear Parameter Estimation, preprint.
PDF
file
- R. B. Kearfott, On Existence and Uniqueness Verification for
Non-Smooth Functions, Reliable
Computing. 8 (4), pp. 267--282 (2002).
PDF
file
- R. B. Kearfott, SIAM Conference on Optimization Validated
Computing 2002 and the Fields Institute Informal Working Group on
Validated Optimization: A Personal View, a report Reliable Computing
8 (5), pp. 419--424 (2002).
PDF file
- R. B. Kearfott, COCOS'02, A Workshop on Global Constrained
Optimization and Constraint Satisfaction, Held October 2--4, 2002,
Sophia--Antipolis, Reliable
Computing 9 (1), pp. 81--87 (2003)
PDF
file
- R. B. Kearfott, Preface, First Validated Computing 2002
Proceedings Issue, Reliable
Computing 9 (2), pp. 89--90 (2003)
PDF
file
- R. B. Kearfott, Preface, Second Validated Computing 2002
Proceedings Issue, Reliable
Computing 9 (5), p. 315 (2003)
PDF
file
- R. B. Kearfott and S. Hongthong, Validated Linear Relaxations and
Preprocessing: Some Experiments, SIAM
Journal
on Optimization 16 (2), pp. 418--433 (2005).
PDF
file
(official reprint from SIAM)
Erratum
(official from SIAM, SIAM J. Optim. 21
(1), pp. 415--416, 2011)
- R. B. Kearfott, M. Neher, S. Oishi, and F. Rico, Libraries,
Tools, and Interactive Systems for Verified Computations: Four Case
Studies, in Numerical Software with Result Verification,
Lecture Notes in Computer Science no. 2991, ed. R. Alt, A.
Frommer, R. B. Kearfott, and W. Luther, Springer Verlag, Heidelberg,
2004. Excerpt containing the part on GlobSol is available:
PDF
file
- V. Kreinovich and R. B. Kearfott, Beyond Convex? Global
Optimization Is Feasible Only for Convex Objective Functions: A
Theorem, Journal
of Global Optimization 33, pp. 617--624 (2005).
PDF file
- S. Hongthong and R. B. Kearfott, Rigorous Linear Overestimators
and Underestimators, technical report.
PDF
file
- R. B. Kearfott, Discussion and Empirical Comparisons of Linear
Relaxations and Alternate Techniques in Validated Deterministic Gobal
Optimization,in Optimization
Methods
and Software 21 (5),
pp.
715--731 (2006).
PDF
file
- R. B. Kearfott, Validated Constraint Solving -- Practicalities,
Pitfalls, and New Developments, in the preliminary proceedings of isiCAD Forum 2004, preprint of an
article in Reliable
Computing 11 (5), pp. 383--391 (2005)
PDF
file
- R. B. Kearfott and Mihye Kim, Hybrid Interval Marching / Branch
and Bound Method for Parametrized Nonlinear Systems, report.
PDF
file
- R. B. Kearfott, Improved and Simplified Validation of Feasible
Points: Inequality and Equality Constrained Problems, preprint.
PDF
file
- R. B. Kearfott, Validated Probing with Linear Relaxations,
preprint.
PDF
file
- R. B. Kearfott, Validated Bounds on Basis Vectors for the Null
Space of a Full Rank Rectangular Matrix, technical report.
Postscript file;DVI
file;PDF
file
- R. B. Kearfott and J. Roy, Verified
Branch and Bound for Singular Linear and Nonlinear Programs -- An
Epsilon-Inflation Process, technical report.
PDF
file
- R. B. Kearfott, Construction of Validated Uniqueness Regions for
Nonlinear Programs in which Convex Subspaces have been Identified,
technical report.
PDF
file
- R. B. Kearfott and S. Hongthong, On Preconditioners and Splitting
in the Interval Gauss--Seidel Method, technical report.
PDF
file
- (related to the above technical report) R. B. Kearfott, A
Comparison of Some Methods for Bounding Connected and Disconnected
Solution Sets of Interval Linear Systems, Computing
82 (1), pp. 77-102 (April, 2008).
PDF
file
*.zip
file
with MATLAB "m" files for the algorithms and experiments(uses INTLAB).
- W. Dean and. B. Kearfott, Reliable Ray Tracing by Linear Interval
Estimations, technical report.
Postscript file;PDF
file
- George Corliss, Christopher Foley, and R. Baker Kearfott, Formulation
for Reliable Analysis of Structural Frames, Reliable
Computing 13 (2), pp. 125-147 (2007)
link to article on the Springer website
- R. B. Kearfott, GlobSol User Guide,
Optimization
Methods
and Software 24
(4-5), pp. 687--708 (August, 2009).
PDF file (of preprint)
- G. F. Corliss, R. Baker Kearfott, N. Nedialkov, and J. D
Pryce, Interval Subroutine
Library Mission, in
Reliable Implementation of Real Number Algorithms
Theory and Practice, Lecture Notes in Computer Science
no. 5045, Springer Verlag, P. Hertling, C. Hoffmann, W. Luther and N.
Revol, eds., 2008, pp. 28-43.
PDF file (of preprint)
- R. B. Kearfott, J. D. Pryce, and N. Revol, Discussions
on an Interval Arithmetic Standard at Dagstuhl Seminar 09021,
in Numerical Validation in Current
Hardware Architectures, Lecture Notes in Computer Science
no. 5492, Springer Verlag, A. Cuyt, W. Kraemer, W. Luther .and P.
Markstein, eds., 2009, pp. 1-6.
PDF file (of preprint)
- R. B. Kearfott, Interval
Computations, Rigour and Non-Rigour in Deterministic Continuous Global
Optimization, Optimization Methods and Software
26 (2), pp. 259--279 (2011).
PDF file (of
preprint)
- R. B. Kearfott, M. T. Nakao, A. Neumaier, S. M. Rump, S. P. Shary, and
P. van Hentenryck, Standardized
Notation in Interval Analysis, Computational Technologies 15 (1), pp. 7-13 (2010).
PDF file
- Julie Roy and R. B. Kearfott, Global Optimization and Singular
Nonlinear Programs: New Techniques, Reliable Computing 15
(3), pp. 242-250 (July, 2011).
PDF
file
- R. B. Kearfott, J. Castille, and G. Tyagi,
A
General Framework for Convexity Analysis and an Alternative to
Branch and Bound in Deterministic Global Optimization,
Journal
of Global Optimization 56 (3),
pp. 765-785 (July, 2013).
PDF
file (of preprint only)
- R. B. Kearfott, J. Castille, and G. Tyagi,
Assessment
of a Non-Adaptive Deterministic Global Optimization Algorithm for
Problems with Low-Dimensional Non-Convex Subspaces,
Optimization
Methods and Software 29
(2), pp. 430-441 (2014).
PDF file (of
early preprint only)
- R. B. Kearfott, Sowmya Muniswami, Yi Wang, Xinyu Li, and Qian Wang, On Smooth Reformulations and Direct
Non-Smooth Computations for Minimax Problems, Journal of Global Optimization
57(4), pp. 1091-1111
(December, 2013).
Link
to the "Online First" copy in the Journal
of Global Optimization. The final publication is available
at link.springer.com.
Preprint of the above article:
PDF file
- R. B. Kearfott, On Rigorous Upper Bounds to a Global
Optimum, Journal of Global Optimization
59 (2-3), pp. 459-476 (July,
2014).
Preprint of the above article:
PDF file
- R. B. Kearfott, An Overview of the
Upcoming IEEE P-1788 Working Group Document: Standard for Interval
Arithmetic, in the Proceedings of the 2013
Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton,
Canada, June 24-28, 2013.
PDF file
- R. B. Kearfott, preprint of Some Observations on Exclusion Regions
in Branch and Bound Algorithms, Journal of Global
Optimization
62
(2), pp. 229-241 (June 2015). The final article
is available at Springer via http://dx.doi.org//10.1007/s10898-014-0248-1.
PDF
file
- Jared T. Guilbeau, Md. Istiaq Hossain, Sam D. Karhbet, Ralph
Baker Kearfott, Temitope S. Sanusi, and Lihong Zhao, A
Review of Computation of Mathematically Rigorous Lower Bounds on
Optima of Linear Programs, accepted for publication in the Journal
of Global Optimization.
The final article is available online from Springer Link at http://link.springer.com/article/10.1007/s10898-016-0489-2.
PDF file with preprint
- W.
Hofschuster, E. D. Popova, and R. B. Kearfott, Bibliography of Prof. Walter Krämer,
in Scientific Computing, Computer
Arithmetic, and Validated Numeric (16th International Symposium,
SCAN 2014, Würzburg, Germany, September 21-26, 2014,
revised selected papers), M. Nehmeier, J. Wolff von Gudenberg, and W.
Tucker, eds., pp. 281-290, 2016.
- Sam Karhbet and R. B. Kearfott, Tools
for Simplicial Branch and Bound in Interval Global Optimization,
Proceedings of SCAN 2016.
(Reliable Computing volume 25, pp. 53--73)
PDF
file
PDF
file of associated presentation
- R. B. Kearfott and Dun Liu, A Brief Review of a Method for Bounds on
Polynomial Ranges over Simplexes, preprint of a chapter
in: Fuzzy Information Processing,
pp. 508--518, Proceedings of the 37th Conference of the North American
Fuzzy Information Processing Society, NAFIPS 2018, Fortaleza, Brazil,
July 4-6, Springer Verlag, 2018.
PDF file
- Diana Paola Lizarralde-Bejarano, Hayriye Gulbudak,
Ralph Baker Kearfott, and Mar??a Eugenia Puerta-Yepes, A novel way to consider uncertainty in epidemiological
models based on ODEs: Considering actual data from
two municipalities in Colombia affected by Dengue, under review for publication.
PDF file
- Ralph Baker Kearfott, Mathematically Rigorous Global Optimization
and Fuzzy Optimization:
A brief comparison of paradigms, methods, similarities
and differences, in Black Box Optimization, Machine Learning
and No-Free Lunch Theorems, Springer Nature Switzerland AG,
Cham, Switzerland, 2020 (book in preparation as of September 2, 2020).
PDF file
Encyclopedia
of
Optimization articles:
- "Interval Analysis: Interval Newton Methods," Encyclopedia
of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 76--78):
PDF
file
- "Interval Analysis: Interval Fixed Point Theory," Encyclopedia
of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 48--51):
PDF
file
- "Interval Analysis: Verifying Feasibility," Encyclopedia
of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 43--45):
PDF
file
- "Interval Analysis: Unconstrained and Constrained Optimization," Encyclopedia of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 40--43):
PDF
file
- "Interval Analysis: Nondifferentiable Problems," Encyclopedia
of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 21--23):
PDF
file
- "Interval Analysis: Intermediate Terms," Encyclopedia
of
Optimization, Kluwer, Dordrecht, Netherlands, 2001,
(vol. 3, pp. 18--21):
PDF
file
PDF Scans of Older Papers
- Doctoral dissertation: R. B. Kearfott, Computing
the
Degree of Maps and a Generalized Method of Bisection,
Department of Mathematics, University of Utah, June, 1977
PDF
file
- R. B. Kearfott, "A proof of Convergence and an Error Bound for the
Method of Bisection in R^{n}," Math.
Comp. 32 (144), pp. 1147--1153 (October, 1978).
PDF
file
- R. B. Kearfott, "An Efficient Degree-Computation Method
for a Generalized Method of Bisection," Numer.
Math. 32, pp. 109--127 (1979).
PDF
file
- R. B. Kearfott, "A Summary of Recent Experiments to Compute the
Topological Degree," in Applied
Nonlinear Analysis, ed. V. Lakshmikantham, Academic Press,
New York, 1979, pp. 627--635.
PDF
file
- R. D. Sidman, R. B. Kearfott, and D. B. Smith, "A Method for
Iidentifying Noise-Free Evoked Potential Components -- Applications of
DLM (Dipole Localization Method) to These Components," IEEE
1980 Frontiers of Engineering in Health Care, pp. 137--140.
(Abstract
is in the IEEE Transactions on
Biomedical Engineering 2, 9 (1980), p. 534.)
PDF
file
- R. B. Kearfott, "A Derivative-Free Arc Continuation Method and a
Bifurcation Technique," in Numerical
Solution of Nonlinear Equations, ed. E. L. Allgower, K.
Glashoff, and H. O. Peitgen, Lecture Notes in Mathematics 878,
Springer, Berlin, 1981, pp. 182--198.
PDF
file
- R. D. Sidman, D. B. Smith, J. S. Henke, R. B. Kearfott, and V.
Giambalvo, "The Use of Equivalent Source Models in EP Research and
Differential Dagnosis," in IEEE 1982 Frontiers of Engineering in
Health Care, ed. B. A. Kohen, pp. 64--70.
PDF
file
- R. B. Kearfott, "Continuation Methods and Parametrized Nonlinear Least
Squares: Techniques and Experiments," in Numerical Methods, Lecture
Notes in Mathematics 1005, ed. V. Pereyra and A. Reinoza, Springer
Verlag, Berlin, 1983, pp. 142--151.
PDF
file
- R. B. Kearfott, "A Sinc Approximation for the Indefinite Integral," Math. Comp. 41 (164),
pp. 559--572 (October, 1983).
PDF
file
R. B. Kearfott, "Some General Bifurcation Techniques," SIAM
J.
Sci. Statist. Comput. 4 (1), pp. 52--68 (March,
1983).
PDF
file
- R. B. Kearfott, "On a General Technique for Finding Directions
Proceeding from Bifurcation Points," in Numerical
Methods for Bifurcation Problems, ed. T. Küpper, H. D.
Mittelmann, and H. Weber, International Series of Numerical Mathematics
70, Birkhäuser, Basel, 1984, pp. 210--218.
PDF
file
- R. B. Kearfott, "Abstract Generalized Bisection and a Cost Bound," Math. Comp. 49
(179), pp. 187--2002 (July, 1987).
PDF
file
- R. B. Kearfott, "Some Tests of Generalized Bisection," ACM
Trans.
Math. Software 13 (3), pp. 197--220 (Sept., 1987).
PDF
file
Corrigienda
- An Interval Newton Method for
Nonlinear Least Squares, manuscript, 1987
PDF
file
- R. D. Sidman, R. B. Kearfott, and C. Schlichting, "The Inverse Problem
of Electroencephalography Assuming Double Layer Neural Generators," in
the Proceedings of the Twelfth IMACS World Congress on Scientific
Computation, vol. 3, vol. 3, R. Vichnevetsky, P. Borne, and J.
Vignes, eds., 1988, pp. 726--728.
PDF
file
- R. B. Kearfott, The Role of Homotopy Techniques in Biomedical
Modeling: a Case Study," in the Proceedings of the Twelfth IMACS
World Congress on Scientific Computation, vol. 3, vol. 3, R.
Vichnevetsky, P. Borne, and J. Vignes, eds., 1988, pp. 732--734.
PDF
file
- C. D. Hill, R. B. Kearfott, and R. D. Sidman, "The inverse problem of
electroencephalography using an imaging technique for simulating
cortical surface data," in the Proceedings of the Twelfth IMACS
World Congress on Scientific Computation, vol. 3, vol. 3, R.
Vichnevetsky, P. Borne, and J. Vignes, eds., 1988, pp. 729--731.
PDF
file
- M. R. Ford, R. D. Sidman, and R. B. Kearfott, "Resting and P300
Auditory Responses in Normal Subjects and Psychiatric Patients: Analysis
Using DLM and Brain Imager," in the Proceedings of the Twelfth IMACS
World Congress on Scientific Computation, vol. 3, vol. 3, R.
Vichnevetsky, P. Borne, and J. Vignes, eds., 1988, pp. 739--740.
PDF
file
- R. D. Sidman, R. B. Kearfott, D. J. Major, C. D. Hill, M. R. Ford, D.
B. Smith, L. Lee, and R. Kramer, "Development and Application of
Mathematical Techniques for the Non-Invasive Localization of the Sources
of Scalp-Recorded Electric Potentials," in Biomedical Systems
Modeling and Simulation, vol. 5 of the IMACS Transactions on
Scientific Computing, J. Eisenfeld and D. S. Levine, eds., J. C.
Baltzer, Basel, 1989, pp. 133--157.
PDF
file
- R. B. Kearfott, "Interval Mathematics Techniques for Control Theory
Computations," in Computation
and Control (pp. 169--178), proceedings of a conference in
Bozeman, Montana, August 1-11, 1988, ed. J. Lund and K. Bowers,
Birkhäuser, Boston, 1989 (Progress in Systems and Control Theory
series).
PDF
file
- R. B. Kearfott, "Interval Arithmetic Methods for Nonlinear Systems and
Nonlinear Optimization: An Introductory Review," pp. 533--542, in Impact
of
Recent Computer Advances on Operations Research, ed. R.
Sharda, B. L. Golden, E. Wasil, O. Balci, and W. Stewart, North-Holland,
New York, 1989.
PDF
file
- R. B. Kearfott, "On Handling Singular Systems with Interval Newton
Methods," in the Proceedings of the Twelfth IMACS World Congress on
Scientific Computation, R. Vichnevetsky, P. Borne, and J. Vignes,
eds., 1988; also in IMACS Annals on Computing and Applied
Mathematics, Numerical and Applied Mathematics, ed. C. Brezinski,
J. C. Baltzer AG, Basel, vol. 1.2 (1989), pp. 653-655.
PDF
file
- R. B. Kearfott, "Interval Newton / Generalized Bisection When There
Are Singularities Near Roots," Annals
of
Operations Research (Special issue on Computational Methods
in Global Optimization) 25, pp. 181--196 (1990).
PDF
file
- R. B. Kearfott, "Preconditioners for the Interval Gauss-Seidel
Method," SIAM
J. Numer. Anal. 27 (3), pp. 804--822 (June, 1990).
PDF file (from JSTOR)
PDF
file for a related 1988 or 1989 technical report comparing different
preconditioners
- R. B. Kearfott and M. Novoa, "Algorithm 681: {INTBIS}, a Portable
Interval Newton/Bisection Package," ACM
Trans. Math. Software 16 (2), pp. 152--157 (June,
1990).
PDF
file
- R.
B. Kearfott, "Interval Arithmetic Techniques in the Computational
Solution of Nonlinear Systems of Equations: Introduction, Examples, and
Comparisons," in Computational Solution of Nonlinear
Systems of Equations, Eugene L. Allgower and Kurt Georg,
editors, proceedings of the Joint AMS-SIAM Summer Seminar,
"Computational Solution of Nonlinear Systems of Equations," held in July
1988 at Colorado State University, Lectures in Applied Mathematics
volume 26, 1990.
PDF
file
- R. B. Kearfott, R. D. Sidman, D. J. Major, and C. D. Hill, "Numerical
Tests of a Method for Simulating Electrical Potentials on the Cortical
Surface," IEEE
Transactions
on Biomedical Engineering 38,
3 (March, 1991), pp. 294--299.
PDF
file
- R. B. Kearfott and Zhaoyun Xing, "An Efficient Interval Step Control
for Two Dimensional Continuation Methods,"
technical report, August, 1992.
PDF
file
Talks
- A Series of Related Talks on GlobSol
- A Brief Introduction to Global Optimization and a Preview of INTOPT_90,
talk given to the Department of Mathematics, Statistics, and Computer
Science, Marquette University, October 16, 1997.
PDF
file
- GlobSol, A Fortran 90 Package for Rigorous Global Search, talk
given at the 1997 International Symposium on Mathematical Programming,
Lausanne, Switzerland, August 25-29, 1997.
PDF file
- The GlobSol Software: An Overview and Examples, presented at
the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.
PDF file
- The GlobSol Project: Rigorous Global Solutions (Overview and
Recent Developments), minisymposium presentation at the 1999
joint SIAM Annual Meeting and Optimization Conference, Atlanta,
Georgia, USA, May 11, 1999.
PDF
file
- Rigorous Global Optimization and the GlobSol Package,
colloquium lecture given to the mathematical sciences department at
the University of Houston-Downtown, September 23, 1999.
PDF
file
- An Overview of the GlobSol Package, talk given at the Fall,
1999 INFORMS meeting,
Philadelphia, Pennsylvania, November 7, 1999.
PDF
file
- An Overview of the GlobSol Package for Verified Global
Optimization, talk given at the Institute of Scientific
Computing, Technical University of Dresden, July, 2000.
PDF
file
- GlobSol: History, Composition, Advice on Use, and Future,
talk given at COCOS'02, first COCONUT International Workshop on global
optimization and constraint propagation, Sophia Antipolis, October 4,
2002, in Lecture Notes in Computer Science no. 2861, Springer
Verlag, pp. 17-31 (2003).
Slides from the talk: PDF
file.
The paper: PDF
file.
- GlobSol Overview, talk
given at Schloß Dagstuhl
Seminar 3041, Numerical Software with Result Verification,
Schloß Dagstuhl, January 23, 2003.
PDF
file
- An overview of the GlobSol Package for Verified Global
Optimization, talk given for the Department of Computing and
Software, McMaster University, Monday, February 8, 2003.
PDF
file
- GlobSol -- Present State and Future Developments, talk given
at the International Workshop on Numerical Verification and its
Applications, Waseda University, Tokyo, February 27, 2007.
PDF
file
- On Utilizing Disconnected Images
within GlobSol's Constraint Propagation Software, talk given
at SCAN 2010, Lyon,
France, September 27-30, 2010.
Slides from the talk: PDF
file.
- Two Roots Good, One Root Better,
presented by Vladik Kreinovich at the Sixteenth Symposium on
Mathematical Programming with Data Perturbations, the George Washington
University, Washington, DC, May 26-27, 1994.
PDF
file
- Interval Methods in Mathematical
Programming, presented by Vladik Kreinovich at the Sixteenth
Symposium on Mathematical Programming with Data Perturbations, the
George Washington University, Washington, DC, May 26-27, 1994.
PDF
file
- Issues for General Users of
Validated Optimization Software: What Does the Answer Mean?
talk given at Schloß Dagstuhl
Seminar 08021, "Numerical Validation in Current Hardware Architectures,"
January 6-11, 2008.
PDF
file
- Interval Arithmetic -- An Elementary Introduction and Successful
Applications, award-winning talk given at a regional meeting of
the Association for Computing Machinery, El-Paso, Texas, 1994.
PDF
file
- Experimental Results: An Interval Step Control for Continuation
Methods, talk given at the AMS-SIAM Summer Seminar in Applied
Mathematics, "Mathematics of Numerical Analysis: Real Number
Algorithms," Park City, Utah, July 17--August 11, 1995.
PDF
file
- Computational Differentiation in Global Optimization Software,
talk given at a minisymposium on the interaction on interval analysis
and computational differentiation, SIAM National Meeting, Stanford,
California, July 14-18, 1997
PDF file
- Automatic Verification of Dynamical System Properties,
presented at an Institute of Mathematics and its Applications workshop
on the Dynamics of Algorithms, University of Minnesota, Minneapolis,
November 17--21, 1997.
PDF file
- Verified Linear and Nonlinear Systems Computations -- Techniques
and Practicalities, presented at the 1998 SIAM Annual Meeting,
Toronto, Canada, July 16, 1998.
PDF file
- Existence and Uniqueness Verification for Singular Zeros of
Nonlinear Systems, presented SCAN'98 (Validated Numerics and
Scientific Computation), Budapest, Hungary, September 22-25, 1998.
PDF
file
- Existence Verification for Singular Zeros of Nonlinear Systems,
presented by Jianwei Dian, minisymposium presentation at the 1999 joint
SIAM Annual Meeting and Optimization Conference, Atlanta, Georgia, USA,
May 13, 1999.
PDF
file
- Efficient Verification of the Topological Index of Real Solutions
to Algebraic Systems, joint with Jianwei Dian, presented at the
2000 Southeastern Section Meeting of the American Mathematical Society
(Meeting #954), April 14-16, 2000, Lafayette, Louisiana. A variant of
this talk was also given at the 2000 AMS-IMS-SIAM summer research
conference on Algorithms and their Complexity for Nonlinear
Problems, July 16 to July 20, 2000, Mt. Holyoke College,
organized by Eugene Allgower, Kurt Georg, and Christopher Sikorski.
PDF
file
- Multivariate Taylor Models in Global Optimization, talk given
at AD 2000, the
third International Conference/Workshop on Automatic Differentiation:
From Simulation to Optimization, June 19-23, 2000, Nice,
France. (Variants were also given at an informal workshop on
Taylor models in automatic differentiation hosted by Martin Berz at the
National Superconducting Cyclotron
Laboratory, Michigan State University, February 17-20, 2000 and as
a colloquium lecture at the University of Louisiana at Lafayette, March
16, 2000)
PDF
file
- Principles of Verified Computations, talk given for the
Mathematics Department of Southeastern
Louisiana University on March 15, 2002. An update and
improvement of several previous talks, this gives an elementary
introduction to interval arithmetic techniques and philosophy, with
additional material on applications and the GlobSol software.
PDF
file
- Interval Linear and Nonlinear Regression -- New Paradigms,
Implementations, and Experiments, or New Ways of Thinking About Data
Fitting (with Jie Yang), talk given at the minisymposium
"Interval Methods in Optimization" at the Seventh
SIAM Conference on Optimization.
PDF
file
- Talks given at Validated
Computing
2002:
- On Existence and Uniqueness Verification for Non-Smooth
Functions
PDF
file
- Twin Estimates for Slopes (with Humberto Muñoz)
PDF
file
- Towards Faster, Better Global Optimization, talk given at the
Global
Optimization Theory Institute, Argonne
National Laboratory, September 10, 2003.
PDF
file
- Short course given June 7 and 8 at the University
of
Witswatersrand, Johannesburg,
South Africa.
HTML
outline
- Validated Constraint Solving: Practicalities, Pitfalls, and New
Developments, talk given at
isiCAD Forum 2004 (jointly with the related workshop ICMP'04)
PDF
file
- Relaxations and Probing: Highly Successful Techniques for
Branch and Bound Search, talk given for the Institute of
Computational Mathematics and Mathematical Geophysics, Siberian Branch
of the Russian Academy of Sciences, and sponsored by LEDAS,
in conjunction with UniPro and ProPro
PDF
file
- Structure and Problem Solving in ISL, talk on the Interval
Subroutine Library project given at Schloß
Dagstuhl
Seminar 06021, Reliable
Implementation of Real Number Algorithms: Theory and Practice,
January 8-13, 2006.
PDF
file
- A Current Assessment of Interval Techniques in Global Optimization,
talk given at the Fields
Institute
Industrial Optimization Seminar, October 3, 2006.
PDF
file
- Degree
Computation
and Global Optimization -- A Personal Perspective, talk
given at "Optimal
Algorithms and Computational Complexity for Numerical Problems," a
conference honorong Prof. Frank Stenger's retirement, Salt Lake City,
Utah, May 7--8, 2007.
- Analysis and Depiction of Solution Sets
to Singular Nonlinear Constrained Optimization Problems,
(Julie Roy's dissertation work), presentation given at the
workshop Algorithmic Differentiation,
Optimization, and Beyond in honor of Andreas Griewank's 60-th
birthday, Nice, France, April 8-9,2010.
PDF
file
- An Overview of the Upcoming IEEE
P-1788 Working Group Document: Standard for Interval Arithmetic,
talk presented at the 2013
Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton,
Canada, June 24-28, 2013.
PDF
file
- The IEEE 754-2008 Floating Point
Standard and its Pending Revision, talk given in
September 2015 at the University of Louisiana applied mathematics
seminar.
- Interval Arithmetic: Fundamentals,
History, and Semantics, talk given November 13, 2016 at
the BIRS
Casa Oaxaca Seminar on Interval Analysis and Constructive Mathematics.
PDF
file with slides
Video
of the presentation
- Tools for Simplicial Branch and
Bound in Interval Global Optimization, talk given at SCAN
2016.
PDF
file
Book Reviews
- of Numerical Toolbox for Verified Computing I: Basic
Numerical Problems, Theory, Algorithms, and Pascal-XSC Programs, by R.
Hammer, M. Hocks, U. Kulisch and D. Ratz (Springer Verlag, 1993), for Zentralblatt
f. Mathematik.
PDF
file
- of Numerica: A modeling Language for Global Optimization, by
P. van Hentenryck, L. Michel, and Y. DeVille, Mathematics
of Computation 67 (224),
pp. 1744-1748 (October, 1998).
PDF
file
- of Computational Complexity and Feasibility of Data Processing and
Interval Computations, by V. Kreinovich, A. Lakeyev, J. Rohn, and
P. Kahl, (Springer Verlag, 1995) Reliable
Computing 4 (4),
pp. 405-409.
PDF
file
- of Real Optimization with SAP
APO by Josef Kallrath and Thomas I Maindl (Springer-Verlag,
Berlin, 2006), SIAM
Review 49 (2), pp. 331-332 (2007).
PDF
file
Proposal
for
standardized interval arithmetic in Fortran (ASCII file)
Acknowledgements
Some of these preprints, publications, and talks were made possible through
one or more of the following grants and contracts
- National Science Foundation Grant CCR-9203730
- National Science Foundation Grant DMS-9701540
- SunSoft Cooperative Research Grant: The GlobSol
project