A bisection method for systems of nonlinear equations

Abstract

This paper describes an algorithm for the solution of a system of nonlinear equations F(X) --- O, where 0 = (0 ..... 0) ~ R", and F is a gwen continuous transformation of n-dimensional simplex S into R"(n >_ 2) The program is based on computation of the topological degree ((leg) of a mapping and a slmplex-b~sectlon scheme. The algorithm is primarily useful for small n(n <_ 5), since the amount of work needed to compute the topological degree for large n is significant. The size of the original simplex is arbitrary, and the algorithm is globally convergent in a residual sense. The algorithm is illustrated on several simplified model problems.