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Several iterative methods with memory using self-accelerators

Author

Listed:
  • Soleymani, F.
  • Lotfi, T.
  • Tavakoli, E.
  • Khaksar Haghani, F.

Abstract

We derive new iterative methods with memory for approximating a simple zero of a nonlinear single variable function. To this end, we first consider several modifications on some existing optimal classes without memory in such a way that their extensions to cases with memory could obtain the higher efficiency index 1214≈1.86120. Furthermore, we construct our main method with memory using three self-accelerators. It is demonstrated that this new scheme possesses the very high efficiency index 7.2381413≈1.93438.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:452-458
    DOI: 10.1016/j.amc.2015.01.045
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    Cited by:

    1. Xiaofeng Wang & Qiannan Fan, 2020. "A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    2. Alicia Cordero & Javier G. Maimó & Juan R. Torregrosa & María P. Vassileva, 2019. "Iterative Methods with Memory for Solving Systems of Nonlinear Equations Using a Second Order Approximation," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    3. Xiaofeng Wang & Yuxi Tao, 2020. "A New Newton Method with Memory for Solving Nonlinear Equations," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    4. 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.
    5. 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.

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