Fast Solution of General Nonlinear Fixed Point Problems

Abstract

In this paper, we develope a general procedure to stabilize the usual Newton method in such a way that algorithms obtained always converge to the unique solution of the problem. The algorthms have two fields of successful application: the case where the operator T Є C1 ∩ H2,∞ and the case where T is polyhedric. In the first case, quadratic convergence is proved; in the second one convergence in a finite number of steps is obtained. Numerical results are shown for an example issued from the field of differential games.