Preprints

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Curriculum vita, including publications that are not available below:

1. PDF file
2. 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A related unpublished report by Manuel Novoa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).
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• 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).
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• 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.
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• 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.
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• 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.
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• 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:
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• 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).
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• 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:
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• 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) 
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• On Verifying Feasibility in Equality Constrained Optimization Problems (technical report to supplement the above).
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• 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.
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• 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))
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• Existence Verification for Singular Zeros of Complex Nonlinear Systems,” SIAM J. Numer. Anal. 38 (2), pp. 360--379 (2000).  (Copyright SIAM.)
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• 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). )
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• 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.
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• 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).
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• 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).
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• R. B. Kearfott and G. W. Walster, Symbolic Preconditioning with Taylor Models:  Some examples,  Reliable Computing  8 (6), pp. 453--468 (2002).
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• H. Muñoz and R. B. Kearfott, Interval Robustness in Nonsmooth Nonlinear Parameter Estimation, preprint.
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• R. B. Kearfott, On Existence and Uniqueness Verification for Non-Smooth Functions, Reliable Computing. 8 (4), pp. 267--282 (2002).
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• 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).
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• 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)
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• R. B. Kearfott, Preface, First Validated Computing 2002 Proceedings Issue, Reliable Computing 9 (2), pp. 89--90 (2003)
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• R. B. Kearfott, Preface, Second Validated Computing 2002 Proceedings Issue, Reliable Computing 9 (5), p. 315 (2003)
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• 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:
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• 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).
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• S. Hongthong and R. B. Kearfott, Rigorous Linear Overestimators and Underestimators, technical report.
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• 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)
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• R. B. Kearfott and Mihye Kim, Hybrid Interval Marching / Branch and Bound Method for Parametrized Nonlinear Systems, report.
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• R. B. Kearfott, Improved and Simplified Validation of Feasible Points: Inequality and Equality Constrained Problems, preprint.
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• R. B. Kearfott, Validated Probing with Linear Relaxations, preprint.
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• 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.
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• R. B. Kearfott and S. Hongthong, On Preconditioners and Splitting in the Interval Gauss--Seidel Method, technical report.
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• (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.
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• 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

• "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):
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• "Interval Analysis: Verifying Feasibility," Encyclopedia of Optimization, Kluwer, Dordrecht,  Netherlands, 2001, (vol. 3, pp. 43--45):
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• "Interval Analysis: Unconstrained and Constrained Optimization," Encyclopedia of Optimization, Kluwer, Dordrecht,  Netherlands, 2001, (vol. 3, pp. 40--43):
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• "Interval Analysis: Nondifferentiable Problems," Encyclopedia of Optimization, Kluwer, Dordrecht,  Netherlands, 2001, (vol. 3, pp. 21--23):
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• "Interval Analysis: Intermediate Terms," Encyclopedia of Optimization, Kluwer, Dordrecht,  Netherlands, 2001, (vol. 3, pp. 18--21):
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• Doctoral dissertation: R. B. Kearfott, Computing the Degree of Maps and a Generalized Method of Bisection, Department of Mathematics, University of Utah, June, 1977
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• 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.)
  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.
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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.
  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.
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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.
  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.
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• The GlobSol Software: An Overview and Examples, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.
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• 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.
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• Rigorous Global Optimization and the GlobSol Package, colloquium lecture given to the mathematical sciences department at the University of Houston-Downtown, September 23, 1999.
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• An Overview of the GlobSol Package, talk given at the Fall, 1999 INFORMS meeting, Philadelphia, Pennsylvania, November 7, 1999.
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• An Overview of the GlobSol Package for Verified Global Optimization, talk given at the Institute of Scientific Computing, Technical University of Dresden, July, 2000.
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• 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.
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• 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.
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• 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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• 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.
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• 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.
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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.
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• 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.
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• 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
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• 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.
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• Verified Linear and Nonlinear Systems Computations -- Techniques and Practicalities, presented at the 1998 SIAM Annual Meeting, Toronto, Canada, July 16, 1998.
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• Existence and Uniqueness Verification for Singular Zeros of Nonlinear Systems, presented SCAN'98 (Validated Numerics and Scientific Computation), Budapest, Hungary, September 22-25, 1998.
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• 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.
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• 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.
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• 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)
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• 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.
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• 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.
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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.
• 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
  

• 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

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