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Efficient n-point iterative methods with memory for solving nonlinear equations

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Abstract

In this paper, we proposed a family of n-point iterative methods with and without memory for solving nonlinear equations. The convergence order of the new n-point iterative methods without memory is 2n requiring n+1 functional evaluations in per full iteration, which implies that the new n-point iterative methods without memory are optimal according to Kung-Traub conjecture. Based on the n-point methods without memory, the n-point iterative methods with memory are obtained by using n+1self-accelerating parameters. The maximal convergence order of the new n-point iterative methods with memory is \((2^{n+1}-1+\sqrt {2^{2(n+1)}+1} )/2\), which is higher than any existing iterative methods with memory. Numerical examples are demonstrated to confirm theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Physics, Bohai University, Jinzhou, 121013, Liaoning, China

    Xiaofeng Wang

  2. College of Sciences, Northeastern University, Shenyang, 110819, Liaoning, China

    Xiaofeng Wang & Tie Zhang

Authors
  1. Xiaofeng Wang
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  2. Tie Zhang
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Correspondence to Xiaofeng Wang.

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Wang, X., Zhang, T. Efficient n-point iterative methods with memory for solving nonlinear equations. Numer Algor 70, 357–375 (2015). https://doi.org/10.1007/s11075-014-9951-8

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  • DOI: https://doi.org/10.1007/s11075-014-9951-8

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