Journal of Applied Mathematics 
Volume 2004 (2004), Issue 2, Pages 127-136
doi:10.1155/S1110757X04307084

Fast intersection methods for the solution of some nonlinear systems of equations

Bernard Beauzamy

Société de Calcul Mathématique, SA, 111 Faubourg Saint Honoré, Paris 75008, France

Received 13 July 2003; Revised 23 February 2004

Abstract

We give a fast method to solve numerically some systems of nonlinear equations. This method applies basically to all systems which can be put in the form UV(X)=Y, where U and V are two possibly nonlinear operators. It uses a modification of Newton's algorithm, in the sense that one projects alternatively onto two subsets. But, here, these subsets are not subspaces any more, but manifolds in a Euclidean space.