AN ANALYSIS OF APPROXIMATE NONLINEAR ELIMINATION

We present a method for solving systems of nonlinear equations suitabl e for problems where convergence of an approximate Newton method is in itially slow. The method, nonlinear elimination (NlEm), eliminates the nonlinear equations and appropriate variables deemed to be causing th e problem. An analysis of the method is given and leads to a detailed algorithm that reduces automatically to an approximate Newton method n ear the root of the system of nonlinear equations. Several examples ar e given that demonstrate the efficacy of the method.