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Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices

Author

Listed:
  • T. Lotfi
  • F. Soleymani
  • Z. Noori
  • A. Kılıçman
  • F. Khaksar Haghani

Abstract

Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we construct a method with memory that increases considerably efficiency index from to . Numerical examples and comparison with the existing methods are included to confirm theoretical results and high computational efficiency.

Suggested Citation

  • T. Lotfi & F. Soleymani & Z. Noori & A. Kılıçman & F. Khaksar Haghani, 2014. "Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-9, September.
  • Handle: RePEc:hin:jnddns:912796
    DOI: 10.1155/2014/912796
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    Cited by:

    1. Chein-Shan Liu & Chih-Wen Chang, 2024. "Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    2. Ekta Sharma & Sunil Panday & Shubham Kumar Mittal & Dan-Marian Joița & Lavinia Lorena Pruteanu & Lorentz Jäntschi, 2023. "Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    3. Chein-Shan Liu & Chih-Wen Chang, 2024. "New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index," Mathematics, MDPI, vol. 12(4), pages 1-22, February.

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