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Two Iterative Methods with Memory Constructed by the Method of Inverse Interpolation and Their Dynamics

Author

Listed:
  • Xiaofeng Wang

    (School of Mathematical Sciences, Bohai University, Jinzhou 121000, China)

  • Mingming Zhu

    (School of Mathematical Sciences, Bohai University, Jinzhou 121000, China)

Abstract

In this paper, we obtain two iterative methods with memory by using inverse interpolation. Firstly, using three function evaluations, we present a two-step iterative method with memory, which has the convergence order 4.5616. Secondly, a three-step iterative method of order 10.1311 is obtained, which requires four function evaluations per iteration. Herzberger’s matrix method is used to prove the convergence order of new methods. Finally, numerical comparisons are made with some known methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods.

Suggested Citation

  • Xiaofeng Wang & Mingming Zhu, 2020. "Two Iterative Methods with Memory Constructed by the Method of Inverse Interpolation and Their Dynamics," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1080-:d:379758
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    References listed on IDEAS

    as
    1. Soleymani, F. & Lotfi, T. & Tavakoli, E. & Khaksar Haghani, F., 2015. "Several iterative methods with memory using self-accelerators," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 452-458.
    2. Lotfi, Taher & Assari, Paria, 2015. "New three- and four-parametric iterative with memory methods with efficiency index near 2," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 1004-1010.
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    Cited by:

    1. Uriel Filobello-Nino & Hector Vazquez-Leal & Jesús Huerta-Chua & Jaime Martínez-Castillo & Agustín L. Herrera-May & Mario Alberto Sandoval-Hernandez & Victor Manuel Jimenez-Fernandez, 2022. "The Enhanced Fixed Point Method: An Extremely Simple Procedure to Accelerate the Convergence of the Fixed Point Method to Solve Nonlinear Algebraic Equations," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    2. Xiaofeng Wang, 2022. "A Novel n -Point Newton-Type Root-Finding Method of High Computational Efficiency," Mathematics, MDPI, vol. 10(7), pages 1-22, April.
    3. Malik Zaka Ullah & Vali Torkashvand & Stanford Shateyi & Mir Asma, 2022. "Using Matrix Eigenvalues to Construct an Iterative Method with the Highest Possible Efficiency Index Two," Mathematics, MDPI, vol. 10(9), pages 1-15, April.

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