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

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 $U\circ V\left(X\right)=Y$, 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.