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Two Optimal General Classes of Iterative Methods with Eighth-Order

Abstract

Two new three-step classes of optimal iterative methods to approximate simple roots of nonlinear equations, satisfying the Kung-Traub’s conjecture, are designed. The development of the methods and their convergence analysis are provided joint with a generalization of both processes. In order to check the goodness of the theoretical results, some concrete methods are extracted and numerical and dynamically compared with some known methods.

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Acknowledgements

The authors would like to render thanks to the reviewers for their comments and suggestions that have improved the readability of the paper.

Author information

Correspondence to Juan R. Torregrosa.

Additional information

This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02.

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Cordero, A., Lotfi, T., Mahdiani, K. et al. Two Optimal General Classes of Iterative Methods with Eighth-Order. Acta Appl Math 134, 61–74 (2014) doi:10.1007/s10440-014-9869-0

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Keywords

  • Multipoint iterative method
  • Nonlinear equation
  • Optimal order
  • Kung-Traub’s conjecture
  • Kung-Traub’s method

Mathematics Subject Classification

  • 65H05
  • 37C75