Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots

Abstract

In this paper, an estimate of the radius of convergence ball of the modified Chebyshev’s method for finding multiple roots of nonlinear equations is provided under the hypotheses that the (m + 1)st derivative f(m+ 1) of function f is Hölder continuous and bounded. The unique ball of a solution is also established. Finally, some examples are provided to show the effectiveness of our results.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11771393, 11632015), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. FX2016073) and the Science Foundation of Taizhou University (Grant No. 2017PY028).

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Correspondence to Yasir Khan.

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Lin, R., Ren, H., Wu, Q. et al. Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots. Vietnam J. Math. (2021). https://doi.org/10.1007/s10013-020-00470-8

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Keywords

  • Chebyshev’s method
  • Nonlinear equations
  • Multiple roots
  • Hölder condition
  • Local convergence
  • Radius of convergence

Mathematics Subject Classification (2010)

  • 65F10
  • 65F50
  • 65H10