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

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  • M. Y. Waziri
  • Z. A. Majid

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.

Suggested Citation

  • M. Y. Waziri & Z. A. Majid, 2013. "An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-6, February.
    • Handle: RePEc:hin:jijmms:814587
    DOI: 10.1155/2013/814587
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    References listed on IDEAS

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    1. M. Y. Waziri & W. J. Leong & M. Mamat, 2012. "A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, March.
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