An algorithm for finding all solutions of a nonlinear system

Let f : X→Rk be a Lipschitz continuous function on a compact subset X⊂Rd. Subdivision algorithms are described that can be used to find all solutions of the equation f(x)=0 that lie in X. Convergence is shown and numerical examples are presented. Modifications of the basic algorithm which speed convergence are given for the case of nondegenerate zeros of a vector field.