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A variant of Chebyshev’s method with sixth-order convergence

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Abstract

In this paper, we present a new variant of Chebyshev’s method for solving non-linear equations. Analysis of convergence shows that the new method has sixth-order convergence. Per iteration the new method requires two evaluations of the function, one of its first derivative and one of its second derivative. Thus the efficiency, in term of function evaluations, of the new method is better than that of Chebyshev’s method. Numerical examples verifying the theory are given.

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Authors and Affiliations

  1. State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, Wuhan, 430072, China

    Jisheng Kou & Yitian Li

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Jisheng Kou

Authors
  1. Jisheng Kou
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  2. Yitian Li
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Correspondence to Jisheng Kou.

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Kou, J., Li, Y. A variant of Chebyshev’s method with sixth-order convergence. Numer Algor 43, 273–278 (2006). https://doi.org/10.1007/s11075-006-9058-y

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  • DOI: https://doi.org/10.1007/s11075-006-9058-y

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