IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2277-d1146158.html
   My bibliography  Save this article

Fractal Newton Methods

Author

Listed:
  • Ali Akgül

    (Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
    Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
    Mathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, 99138 Nicosia, Turkey)

  • David Grow

    (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA)

Abstract

We introduce fractal Newton methods for solving f ( x ) = 0 that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

Suggested Citation

  • Ali Akgül & David Grow, 2023. "Fractal Newton Methods," Mathematics, MDPI, vol. 11(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2277-:d:1146158
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2277/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2277/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Brouers, F. & Sotolongo-Costa, O., 2006. "Generalized fractal kinetics in complex systems (application to biophysics and biotechnology)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 165-175.
    2. Xiaofeng Wang & Yuxi Tao, 2020. "A New Newton Method with Memory for Solving Nonlinear Equations," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    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. Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.

    More about this item

    Keywords

    fractal derivative; fractal Newton methods;

    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:gam:jmathe:v:11:y:2023:i:10:p:2277-:d:1146158. 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.