Finding all solutions of nonlinear equations using the dual simplex method

Authors:
Kiyotaka Yamamura;Tsuyoshi Fujioka
Affiliations:
Department of Electrical, Electronic, and Communication Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan;Department of Electrical, Electronic, and Communication Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

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Abstract

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.