Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 127-136

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

Copyright © 2004 Bernard Beauzamy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.