An algorithm for finding all zeros of vector functions

Abstract

Computing a zero of a continuous function is an old and extensively researched problem in numerical computation. In this paper, we present an efficient subdivision algorithm for finding all real roots of a function in multiple variables. This algorithm is based on a simple computationally verifiable necessity test for the existence of a root in any compact set. Both theoretical analysis and numerical simulations demonstrate that the algorithm is very efficient and reliable. Convergence is shown and numerical examples are presented. © 2008 Australian Mathematical Society.