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

Mohammed Yusuf Waziri | Zendy; Zanariah Abdul Majid | Zendy

Open Access

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

Author(s) -

Mohammed Yusuf Waziri,

Zanariah Abdul Majid

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/814587

Subject(s) - line search , mathematics , secant method , diagonal , backtracking , convergence (economics) , predictor–corrector method , nonlinear system , scheme (mathematics) , line (geometry) , matrix (chemical analysis) , diagonal matrix , newton's method , mathematical optimization , algorithm , computer science , path (computing) , mathematical analysis , geometry , physics , materials science , quantum mechanics , economics , composite material , programming language , economic growth

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

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