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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
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    References listed on IDEAS

    as
    1. Xiaofeng Wang & Yuxi Tao, 2020. "A New Newton Method with Memory for Solving Nonlinear Equations," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    fractal derivative; fractal Newton methods;

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