Lipschitz condition for finding real roots of a vector function

Abstract

Computing real roots of a continuous function is an old and extensively researched problem in numerical computation. Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a root condition that can be applied to each cell in the domain. In the present paper, we consider Lipschitz functions of order α and give the root condition for the exclusion algorithms. Furthermore, we investigate convergence and computational complexity for such algorithms and illustrate their performance by a numerical example.