IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v410y2021ics009630032100504x.html
   My bibliography  Save this article

On the approximation of mth power divided differences preserving the local order of convergence

Author

Listed:
  • Amiri, Abdolreza
  • Argyros, Ioannis K.

Abstract

In this paper, some extensions are presented for a new technique to construct a family of divided differences that has been proposed previously. By applying a new definition for local order of convergence and presenting a comprehensive analysis, the relation between local order of convergence and R-order and Q-order is investigated. We also propose a new technique to approximate the elements of the developed divided differences. The divided differences are approximated by using the new scheme and are replaced in some iterative methods. Numerical experiments show that new derivative-free iterative methods obtained in this way are with high order of convergence. Numerical results confirm the theoretical results and indicate the efficiency and robustness of the new Jacobian-free methods.

Suggested Citation

  • Amiri, Abdolreza & Argyros, Ioannis K., 2021. "On the approximation of mth power divided differences preserving the local order of convergence," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s009630032100504x
    DOI: 10.1016/j.amc.2021.126415
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032100504X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126415?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. Miquel Grau-Sánchez & Miquel Noguera & José M. Gutiérrez, 2014. "Frozen Iterative Methods Using Divided Differences “à la Schmidt–Schwetlick”," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 931-948, March.
    2. Amiri, Abdolreza & Cordero, Alicia & Taghi Darvishi, M. & Torregrosa, Juan R., 2018. "Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 43-57.
    3. Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    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. Francisco I. Chicharro & Rafael A. Contreras & Neus Garrido, 2020. "A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.
    2. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2019. "Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    3. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi, 2021. "Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    4. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.

    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:410:y:2021:i:c:s009630032100504x. 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.