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A multidimensional dynamical approach to iterative methods with memory

Author

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  • Campos, Beatriz
  • Cordero, Alicia
  • Torregrosa, Juan R.
  • Vindel, Pura

Abstract

A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made. We have designed new methods with memory from Steffensen’ or Traub’s schemes, as well as from a parametric family of iterative procedures of third- and fourth-order of convergence. We study the local order of convergence of the new iterative methods with memory.

Suggested Citation

  • Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2015. "A multidimensional dynamical approach to iterative methods with memory," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 701-715.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:701-715
    DOI: 10.1016/j.amc.2015.09.056
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    Citations

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    Cited by:

    1. Cordero, Alicia & Soleymani, Fazlollah & Torregrosa, Juan R. & Haghani, F. Khaksar, 2017. "A family of Kurchatov-type methods and its stability," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 264-279.
    2. 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.
    3. F. I. Chicharro & A. Cordero & J. R. Torregrosa & M. P. Vassileva, 2017. "King-Type Derivative-Free Iterative Families: Real and Memory Dynamics," Complexity, Hindawi, vol. 2017, pages 1-15, October.
    4. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2020. "Impact on Stability by the Use of Memory in Traub-Type Schemes," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    5. Alicia Cordero & Javier G. Maimó & Juan R. Torregrosa & María P. Vassileva, 2023. "Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    6. Alicia Cordero & Beny Neta & Juan R. Torregrosa, 2021. "Memorizing Schröder’s Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    7. Ramandeep Behl & Alicia Cordero & Juan R. Torregrosa & Sonia Bhalla, 2021. "A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems," Mathematics, MDPI, vol. 9(17), pages 1-16, September.
    8. 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.

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