Journal of Applied Mathematics
Volume 2013 (2013), Article ID 875935, 6 pages
http://dx.doi.org/10.1155/2013/875935
Research Article

An Improved Diagonal Jacobian Approximation via a New Quasi-Cauchy Condition for Solving Large-Scale Systems of Nonlinear Equations

Mohammed Yusuf Waziri1,2 and Zanariah Abdul Majid1,3

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematical Sciences, Faculty of Science, Bayero University, Kano PMB 3011, Nigeria
3Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 8 August 2012; Revised 14 December 2012; Accepted 15 December 2012

Academic Editor: Turgut Öziş

Copyright © 2013 Mohammed Yusuf Waziri and Zanariah Abdul 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.

Abstract

We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods.