IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v284y2016icp195-208.html
   My bibliography  Save this article

Dynamics of a multipoint variant of Chebyshev–Halley’s family

Author

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

Abstract

In this paper, a complex dynamical study of a parametric Chebyshev–Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of the family. We also calculate the critical points building their corresponding parameter planes which allow us to analyze the qualitative behavior of this family. Moreover, we locate some dynamical planes showing different pathological aspects of this family.

Suggested Citation

  • Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2016. "Dynamics of a multipoint variant of Chebyshev–Halley’s family," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 195-208.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:195-208
    DOI: 10.1016/j.amc.2016.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302016
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.03.009?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Argyros, Ioannis K. & Magreñán, Á. Alberto, 2015. "On the convergence of an optimal fourth-order family of methods and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 336-346.
    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. Argyros, Ioannis K. & Kansal, Munish & Kanwar, Vinay & Bajaj, Sugandha, 2017. "Higher-order derivative-free families of Chebyshev–Halley type methods with or without memory for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 224-245.
    2. Petković, I. & Herceg, Ð., 2017. "Symbolic computation and computer graphics as tools for developing and studying new root-finding methods," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 95-113.
    3. Ioannis K. Argyros & Ángel Alberto Magreñán & Lara Orcos & Íñigo Sarría, 2019. "Unified Local Convergence for Newton’s Method and Uniqueness of the Solution of Equations under Generalized Conditions in a Banach Space," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    4. Ramandeep Behl & Ioannis K. Argyros, 2020. "Local Convergence for Multi-Step High Order Solvers under Weak Conditions," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    5. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2015. "Construction of fourth-order optimal families of iterative methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 89-101.
    6. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros & Ángel Alberto Magreñán, 2019. "On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems," Mathematics, MDPI, vol. 7(6), pages 1-27, May.
    7. Behl, Ramandeep & Cordero, Alicia & Motsa, S.S. & Torregrosa, Juan R., 2015. "On developing fourth-order optimal families of methods for multiple roots and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 520-532.
    8. García Calcines, José M. & Gutiérrez, José M. & Hernández Paricio, Luis J. & Rivas Rodríguez, M. Teresa, 2015. "Graphical representations for the homogeneous bivariate Newton’s method," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 988-1006.
    9. 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.
    10. 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.
    11. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2017. "Stable high-order iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 70-88.
    12. Min-Young Lee & Young Ik Kim & Beny Neta, 2019. "A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points," Mathematics, MDPI, vol. 7(6), pages 1-26, June.
    13. Chun, Changbum & Neta, Beny, 2015. "Basins of attraction for several third order methods to find multiple roots of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 129-137.
    14. Young Hee Geum & Young Ik Kim, 2020. "Computational Bifurcations Occurring on Red Fixed Components in the λ -Parameter Plane for a Family of Optimal Fourth-Order Multiple-Root Finders under the Möbius Conjugacy Map," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    15. Young Hee Geum & Young Ik Kim & Beny Neta, 2018. "Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics," Mathematics, MDPI, vol. 7(1), pages 1-32, December.
    16. 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.
    17. 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.
    18. Chun, Changbum & Neta, Beny, 2016. "Comparison of several families of optimal eighth order methods," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 762-773.
    19. Hueso, José L. & Martínez, Eulalia & Gupta, D.K. & Cevallos, Fabricio, 2018. "A note on “Convergence radius of Osada’s method under Hölder continuous condition”," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 689-699.
    20. Chun, Changbum & Neta, Beny, 2015. "Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 277-292.

    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:eee:apmaco:v:284:y:2016:i:c:p:195-208. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.