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The convergence ball and error analysis of the two-step Secant method

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Abstract

Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order, we obtain an estimate of the radius of the convergence ball for the two-step secant method. Moreover, we also provide an error estimate that matches the convergence order of the two-step secant method. At last, we give an application of the proposed theorem.

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Authors and Affiliations

  1. Department of Mathematics, Taizhou University, Linhai, 317000, China

    Rong-fei Lin

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Qing-biao Wu, Yasir Khan & Lu Liu

  3. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310012, China

    Min-hong Chen

Authors
  1. Rong-fei Lin
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  2. Qing-biao Wu
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  3. Min-hong Chen
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  4. Yasir Khan
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  5. Lu Liu
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Corresponding author

Correspondence to Qing-biao Wu.

Additional information

This work is supported by National Natural Science Foundation of China (11771393, 11371320, 11632015), Zhejiang Natural Science Foundation (LZ14A010002, LQ18A010008) and Scientific Research Fund of Zhejiang Provincial Education Department (FX2016073).

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Lin, Rf., Wu, Qb., Chen, Mh. et al. The convergence ball and error analysis of the two-step Secant method. Appl. Math. J. Chin. Univ. 32, 397–406 (2017). https://doi.org/10.1007/s11766-017-3487-3

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  • DOI: https://doi.org/10.1007/s11766-017-3487-3

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