R. Baker Kearfott
Professor

Contact:
Office: 101A Foster
Phone: 337-482-5270
E-mail: rbk@louisiana.edu
Home page: http://interval.louisiana.edu/kearfott.html

Degrees:
Ph.D. 1977 University of Utah
M.S. 1974 University of Utah
B.S. 1972 University of Utah

Statement:
Current interests include numerical analysis with automatic result verification, especially global optimization and nonlinear algebraic systems, and scientific software development. Aside from research reflected in publications and invited lectures, professional activities have included: (1) scientific committee membership for various conferences, as well as main organizer of a major conference (2) member of the Fortran programming language standardization committee.

Selected research publications:

• Discussion and Empirical Comparisons of Linear Relaxations and Alternate Techniques in Validated Deterministic Global Optimization, Optimization Methods and Software, 21 (2006), 715-731.
• Validated Linear Relaxations and Preprocessing: Some Experiments (with S. Hongthong), SIAM Journal on Optimization, 16 (2005), 418-433.
• Beyond Convex? Global Optimization Is Feasible Only for Convex Objective Functions: A Theorem (with V. Kreinovich), Journal of Global Optimization, 33 (2005), 617-624.
• Existence Verification for Singular and Non-Smooth Zeros of Real Nonlinear Systems (with J. Dian), Math. Comp., 72 (2003), 757--766.
• On Existence and Uniqueness Verification for Non-Smooth Functions, Reliable Computing, 8 (2002), 267-282.
• An Example of Singularity in Global Optimization, Reliable Computing, 7 (2001), 425-429.
• Existence verification for singular zeros of complex nonlinear systems, joint with J. Dian and A. Neumaier, SIAM J. Numer. Anal., 38 (2000), 360-379.
• On stopping criteria in verified nonlinear systems or optimization algorithms, joint with G. W. Walster, ACM Trans. Math. Software, 26 (2000), 323-351.
• On proving existence of feasible points in equality constrained optimization problems, Math. Prog., 83 (1998), 89-100.
• Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems, SIAM J. Sci. Comput., 18 (1997), 574-594.
• Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.
• A Fortran 90 environment for research and prototyping of enclosure algorithms for constrained and unconstrained nonlinear equations, ACM Trans. Math. Software, 21 (1995), 63-78.
• Algorithm 737: INTLIB, A portable Fortran-77 elementary function library (with M. Dawande, K. Du and C. Hu), ACM Trans. Math. Software, 20 (1994), 447-459.
• The cluster problem in multivariate global optimization (with K. Du), Journal of Global Optimization, 5 (1994), 253-265.
• An interval step control for continuation methods (with Z. Xing), SIAM J. Numer. Anal., 31 (1994), 892-914.
• Numerical tests of a method for simulating electrical potentials on the cortical surface (with R. D. Sidman, D. J. Major, and C. D. Hill), IEEE Trans. Biomed. Engrg., 38 (1991), 294-299.
• Preconditioners for the interval Gauss-Seidel method, SIAM J. Numer. Anal., 27 (1990), 804-822.
• Algorithm 681: INTBIS, a portable interval Newton/bisection package (with Manuel Novoa), ACM Trans. Math. Software, 16 (1990), 152-157.
• A sinc approximation for the indefinite integral, Math. Comp., 41 (1983), 559-572.
• An efficient degree-computation method for a generalized method of bisection, Numer. Math., 32 (1979), 109-127.
• Computing the Degree of Maps and a Generalized Method of Bisection, doctoral dissertation, University of Utah (1977).