An analysis of approximate nonlinear elimination

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