Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 258072, 5 pages
http://dx.doi.org/10.1155/2013/258072
Research Article

Solving Separable Nonlinear Equations Using LU Factorization

Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA

Received 15 May 2013; Accepted 4 June 2013

Academic Editors: R. Barrio and B. Djafari Rouhani

Copyright © 2013 Yun-Qiu Shen and Tjalling J. Ypma. 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.

Abstract

Separable nonlinear equations have the form where the matrix and the vector are continuously differentiable functions of and . We assume that and has full rank. We present a numerical method to compute the solution for fully determined systems ( ) and compatible overdetermined systems ( ). Our method reduces the original system to a smaller system of equations in alone. The iterative process to solve the smaller system only requires the LU factorization of one matrix per step, and the convergence is quadratic. Once has been obtained, is computed by direct solution of a linear system. Details of the numerical implementation are provided and several examples are presented.