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Memorizing Schröder’s Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity

Author

Listed:
  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
    These authors contributed equally to this work.)

  • Beny Neta

    (Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
    These authors contributed equally to this work.)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
    These authors contributed equally to this work.)

Abstract

In this paper, we propose, to the best of our knowledge, the first iterative scheme with memory for finding roots whose multiplicity is unknown existing in the literature. It improves the efficiency of a similar procedure without memory due to Schröder and can be considered as a seed to generate higher order methods with similar characteristics. Once its order of convergence is studied, its stability is analyzed showing its good properties, and it is compared numerically in terms of their basins of attraction with similar schemes without memory for finding multiple roots.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2570-:d:655435
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    References listed on IDEAS

    as
    1. 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.
    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. Saima Akram & Faiza Akram & Moin-ud-Din Junjua & Misbah Arshad & Tariq Afzal & Ghulam Mustafa, 2021. "A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, March.
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