IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p540-d342141.html
   My bibliography  Save this article

A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

Author

Listed:
  • Xiaofeng Wang

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

  • Qiannan Fan

    (School of Mathematics and Physics, Bohai University, Jinzhou 121000, China)

Abstract

In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:540-:d:342141
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/540/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/540/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. Ullah, M. Zaka & Kosari, S. & Soleymani, F. & Haghani, F. Khaksar & S. Al-Fhaid, A., 2016. "A super-fast tri-parametric iterative method with memory," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 486-491.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    4. Xiaofeng Wang & Yuxi Tao, 2020. "A New Newton Method with Memory for Solving Nonlinear Equations," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:540-:d:342141. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.