Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 127-136
Fast intersection methods for the solution of some nonlinear systems of equations
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 , where and 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.