An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations. (19th February 2013)

• Record Type: Journal Article
• Authors: Waziri, M. Y.; Majid, Z. A.
• Other Names: Ricci Paolo Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2013(2013)
• Publication Date: 2013-02-19
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2013/814587
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : 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.