IDEAS home Printed from https://ideas.repec.org/a/hin/complx/2713145.html
   My bibliography  Save this article

King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

Author

Listed:
  • F. I. Chicharro
  • A. Cordero
  • J. R. Torregrosa
  • M. P. Vassileva

Abstract

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:2713145
    DOI: 10.1155/2017/2713145
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/2713145.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/2713145.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/2713145?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hueso, José L. & Martínez, Eulalia & Teruel, Carles, 2015. "Derivative free iterative methods for nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 955-966.
    2. Magreñán, Á. Alberto & Cordero, Alicia & Gutiérrez, José M. & Torregrosa, Juan R., 2014. "Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 49-61.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Prem B. Chand & Francisco I. Chicharro & Neus Garrido & Pankaj Jain, 2019. "Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications," Mathematics, MDPI, vol. 7(10), pages 1-21, October.

    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. 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.
    2. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2016. "A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 120-140.
    3. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "On developing a higher-order family of double-Newton methods with a bivariate weighting function," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 277-290.
    4. 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.
    5. 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.
    6. Chun, Changbum & Neta, Beny, 2016. "An analysis of a Khattri’s 4th order family of methods," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 198-207.
    7. Geum, Young Hee & Kim, Young Ik & Magreñán, Á. Alberto, 2016. "A biparametric extension of King’s fourth-order methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 254-275.
    8. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 387-400.
    9. 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.
    10. 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.
    11. 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.
    12. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2017. "A family of optimal quartic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 1-21.
    13. 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.
    14. Lee, Min-Young & Ik Kim, Young & Alberto Magreñán, Á., 2017. "On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-to function ratio," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 564-590.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:2713145. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.