ALGORITHM FOR PIECEWISE-LINEAR APPROXIMATION OF AN IMPLICITLY DEFINED MANIFOLD.

Abstract

A simplicial method is used to approximate the solution manifold to a system of nonlinear equations, H(x) ) equals theta , where H:R**N** plus **K yields R**N. The method begins at a point chi //0 in the solution set where the derivative DH( chi //0) is of full rank. Given any epsilon greater than 0, a piecewise linear manifold is constructed along which parallel H( chi ) parallel // infinity less than epsilon . An algorithm is presented to carry out this construction in an efficient fashion.