Journal of Applied Mathematics
Volume 2012 (2012), Article ID 348654, 9 pages
http://dx.doi.org/10.1155/2012/348654
Research Article

A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations

M. Y. Waziri,1,2 W. J. Leong,1 and M. Mamat3

1Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Malaysia
2Department of Mathematics, Faculty of Science, Bayero University Kano, Kano 2340, Nigeria
3Department of Mathematics, Faculty of Science and Technology, Malaysia Terengganu University, Kuala Lumpur 21030 Terengganu, Malaysia

Received 9 November 2011; Revised 11 January 2012; Accepted 16 January 2012

Academic Editor: Renat Zhdanov

Copyright © 2012 M. Y. Waziri et al. 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

We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.