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Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications

Author

Listed:
  • Ioannis K. Argyros

    (Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA)

  • Christopher Argyros

    (Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA)

  • Johan Ceballos

    (Facultad de Ingeniería y Ciencias Aplicadas, Universidad de Las Américas, Quito 170124, Ecuador)

  • Daniel González

    (Facultad de Ingeniería y Ciencias Aplicadas, Universidad de Las Américas, Quito 170124, Ecuador)

Abstract

Comparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria of these methods under the same conditions as in previous papers. It turns out that the following advantages are shown: enlarged convergence domain; tighter error estimates and a more precise information on the location of the solution. Advantages are obtained under the same or at least as tight Lipschitz constants, which are specializations of earlier ones. Hence, the applicability of these methods is extended. Numerical experiments complete this study.

Suggested Citation

  • Ioannis K. Argyros & Christopher Argyros & Johan Ceballos & Daniel González, 2022. "Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2851-:d:884975
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    References listed on IDEAS

    as
    1. Ioannis K. Argyros, 2021. "Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
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