Preprints

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Curriculum vita, including publications that are not available below:

1. Postscript file;
2. DVI file ;
3. PDF file
4. Send mail to rbk@louisiana.edu for further information.

Please cite properly any of this material that you use.

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: Chapters 1 through 3
PDF file: Chapter 4
PDF file: Chapters_5_to_6
PDF file: Chapters_6_to_end
• R. B. Kearfott, "A proof of Convergence and an Error Bound for the Method of Bisection in Rⁿ,"  Math. Comp. 32 (144), pp. 1147--1153 (October, 1978).

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• R. B. Kearfott, "An  Efficient  Degree-Computation Method for a Generalized Method of Bisection," Numer. Math. 32, pp. 109--127 (1979).

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• R. B. Kearfott, "A Sinc Approximation for the Indefinite Integral," Math. Comp. 41 (164), pp. 559--572 (October, 1983).

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R. B. Kearfott, "Some General Bifurcation Techniques," SIAM J. Sci. Statist. Comput. 4 (1), pp. 52--68 (March, 1983).
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• 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.

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• R. B. Kearfott, "Abstract Generalized Bisection and a Cost Bound," Math. Comp. 49 (179), pp. 187--2002 (July, 1987).

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• R. B. Kearfott, "Some Tests of Generalized Bisection," ACM Trans. Math. Software 13 (3), pp. 197--220 (Sept., 1987).

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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).

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• 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.

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• 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.

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• 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).

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• R. B. Kearfott, "Preconditioners for the Interval Gauss-Seidel Method," SIAM J. Numer. Anal. 27 (3), pp. 804--822 (June, 1990).

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• 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).

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• 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.

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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.

Postscript file; DVI file; 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.

Postscript file;DVI file; PDF file
• The GlobSol Software: An Overview and Examples, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.

Postscript file; DVI file; 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.

Postscript file; DVI file; 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.

Postscript file; DVI file; PDF file
• An Overview of the GlobSol Package, talk given at the Fall, 1999 INFORMS meeting, Philadelphia, Pennsylvania, November 7, 1999.

Postscript file; DVI file; 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.

Postscript file; DVI file; 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: Postscript file; DVI file;PDF file.
The paper: Postscript file; DVI file;PDF file.
• GlobSol Overview, talk given at Schloß Dagstuhl Seminar 3041, Numerical Software with Result Verification,  Schloß Dagstuhl, January 23, 2003.

Postscript file; DVI file;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.

Postscript file; DVI file;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.

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• 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.

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• 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.

Postscript file; DVI file;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.

Postscript file; DVI file; 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

Postscript file; DVI file; 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.

Postscript file; DVI file; PDF file
• Verified Linear and Nonlinear Systems Computations -- Techniques and Practicalities, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.

Postscript file; DVI file; 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.

Postscript file; DVI file; 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.

Postscript file; DVI file; 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.

Postscript file; DVI 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)

Postscript file; DVI file; 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.

Postscript file; DVI file; 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.

Postscript file; DVI file (may not contain all figures); PDF file
•  Talks given at Validated Computing 2002:
• On Existence and Uniqueness Verification for Non-Smooth Functions

Postscript file; DVI file (may not contain all figures); PDF file
• Twin Estimates for Slopes (with Humberto Muñoz)

Postscript file; DVI file (may not contain all figures); PDF file
• Towards Faster, Better Global Optimization, talk given at the Global Optimization Theory Institute, Argonne National Laboratory, September 10, 2003.

Postscript file; DVI file; 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)

Postscript file;DVI file;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

Postscript file;DVI file;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.

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• A Current Assessment of Interval Techniques in Global Optimization, talk given at the Fields Institute Industrial Optimization Seminar, October 3, 2006.

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• 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.

• of Numerical Toolbox for Verified Computing I, by R. Hammer, M. Hocks, U. Kulisch and D. Ratz, for Zentralblatt f. Mathematik.

Postscript file; DVI file; PDF file
• of Numerica: A modeling Language for Global Optimization, by P. van Hentenryck, L. Michel, and Y. DeVille, for the Mathematics of Computation.

Postscript file; DVI file; PDF file
• of Computational Complexity and Feasibility of Data Processing and Interval Computations, by V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, for Reliable Computing.

Postscript file; DVI file; PDF file

• National Science Foundation Grant CCR-9203730
• National Science Foundation Grant DMS-9701540
• SunSoft Cooperative Research Grant:  The GlobSol  project