Partially Updated Switching-Method for systems of nonlinear equations

A hybrid method for solving systems of n nonlinear equations is given. The method does not use derivative information and is especially attractive when good starting points are not available and the given system is expensive to evaluate. It is shown that, after a few steps, each iteration requires (2k + 1) function evaluations where k, 1 ⩽ k ⩽ n, is chosen so as to have an efficient algorithm. Global convergence results are given and superlinear convergence is established. Some numerical results show the numerical performance of the proposed method.