An algorithm for finding all solutions of a nonlinear system

[摘要] Let f : X --> R-k be a Lipschitz continuous function on a compact subset X subset of R-d. 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. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-12-15

[关键词] subdivision algorithm;Newton's method