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A derivative-free conjugate residual method using secant condition for general large-scale nonlinear equations

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Abstract

A fully derivative-free conjugate residual method, using secant condition, is introduced to solve general large-scale nonlinear equations. Under some conditions, global and linear convergence of the proposed method is established by adopting some backtracking type line search. Some numerical results compared with two existing derivative-free methods are reported to show its efficiency.

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Acknowledgements

We would like to thank the editor and the referees whose very helpful suggestions led to much improvement of this paper.

Funding

This work was supported by the SRF (13B137) of Hunan Provincial Education Department, the NSF (14JJ3084) of Hunan Province and Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410004, China

    Li Zhang

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  1. Li Zhang
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Correspondence to Li Zhang.

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Zhang, L. A derivative-free conjugate residual method using secant condition for general large-scale nonlinear equations. Numer Algor 83, 1277–1293 (2020). https://doi.org/10.1007/s11075-019-00725-7

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  • DOI: https://doi.org/10.1007/s11075-019-00725-7

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