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Convergence Properties of an Iterative Method for Solving Symmetric Non-linear Equations

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Abstract

We introduce an iterative method for solving symmetric systems of non-linear equations without computing Jacobian and gradient using the special structure of the underlying function. This derivative-free feature makes it solve relatively large-scale problems. We show that the proposed method has global and linear convergence properties under appropriate conditions. We also report some numerical results to show its efficiency.

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Acknowledgments

The authors thank the editor and the anonymous referees for their valuable comments. This work was supported in part by the NSF (11371073) of China, the Key Project of the Scientific Research Fund (12A004) of the Hunan Provincial Education Department, and the NSF (13JJ4062) of Hunan Province.

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Authors and Affiliations

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

    Weijun Zhou & Dongmei Shen

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  1. Weijun Zhou
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  2. Dongmei Shen
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Correspondence to Weijun Zhou.

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Communicated by Nobuo Yamashita.

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Zhou, W., Shen, D. Convergence Properties of an Iterative Method for Solving Symmetric Non-linear Equations. J Optim Theory Appl 164, 277–289 (2015). https://doi.org/10.1007/s10957-014-0547-1

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  • DOI: https://doi.org/10.1007/s10957-014-0547-1

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