International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 814587, 6 pages
Research Article

An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematical Sciences, Faculty of Science, Bayero University Kano, Kano, Nigeria
3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 28 September 2012; Revised 24 December 2012; Accepted 7 January 2013

Academic Editor: Paolo Ricci

Copyright © 2013 M. Y. Waziri and Z. A. Majid. 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.


Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.