A new exclusion test

Authors:
Kurt Georg
Affiliations:
Department of Mathematics, Colorado State University, Fort Collins, CO
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

Citing 7
Cited 4

A computational method for finding all the roots of a vector function

Applied Mathematics and Computation
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++

ACM Transactions on Mathematical Software (TOMS)
A cell exclusion algorithm for determining all the solutions of a nonlinear system of equations

Applied Mathematics and Computation
Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Systems

SIAM Journal on Scientific Computing
A general CDC formulation for specializing the cell exclusion algorithms of finding all zeros of vector functions

Applied Mathematics and Computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation

ACM Transactions on Mathematical Software (TOMS)
On the complexity of exclusion algorithms for optimization

Journal of Complexity

Numerical analysis of a bisection-exclusion method to find zeros of univariate analytic functions

Journal of Complexity
A new exclusion test for finding the global minimum

Journal of Computational and Applied Mathematics
Finding all solutions of separable systems of piecewise-linear equations using integer programming

Journal of Computational and Applied Mathematics
Lipschitz condition for finding real roots of a vector function

Journal of Computational Methods in Sciences and Engineering

Quantified Score

Hi-index	0.00

Visualization

Abstract

Exclusion tests are a well-known tool for obtaining all solutions of a nonlinear system of equations, see, e.g., the work of Krawczyk or Moore. Recently, Yamamura and collaborators have developed Linear Programming exclusion tests that turned out to be highly successful for nonlinear problems in electrical networking. The author has developed higher order exclusion tests based on Taylor expansions. In the present paper it is shown that the ideas behind both approaches can be combined: We present a new class of higher order Linear Programming exclusion tests, investigate their computational complexity, and illustrate their performance on several examples.