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Convergence of the modified Halley’s method for multiple zeros under Hölder continuous derivative

Abstract

In this paper, the estimate of the radius of the convergence ball of the modified Halley’s method for finding multiple zeros of nonlinear equations is provided under the hypotheses that the derivative f (m + 1) of function f is Hölder continuous, and f (m + 1) is bounded. The uniqueness ball of solution is also established. Finally, some examples are provided to show applications of our theorem.

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Correspondence to Weihong Bi.

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Bi, W., Ren, H. & Wu, Q. Convergence of the modified Halley’s method for multiple zeros under Hölder continuous derivative. Numer Algor 58, 497–512 (2011). https://doi.org/10.1007/s11075-011-9466-5

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Keywords

  • Halley’s method
  • Multiple zeros
  • Hölder condition
  • Local convergence
  • Radius of convergence

Mathematics Subject Classifications (2010)

  • 41A25
  • 65G99
  • 65H99
  • 49M15
  • 47J25