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A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II

Author

Listed:
  • Samundra Regmi

    (Department of Mathematics, University of Houston, Houston, TX 77204, USA)

  • Ioannis K. Argyros

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

  • Santhosh George

    (Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575 025, India)

  • Michael I. Argyros

    (Department of Computer Science, University of Oklahoma, Norman, OK 73019, USA)

Abstract

This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is expressed explicitly in turns of the Lipschitz or Hölder constants and the convergence order 1 + p is shown for p ∈ ( 0 , 1 ] . The first feature becomes attainable by further simplifying proofs of convergence criteria. The second feature is possible by choosing a bit larger upper bound on the smallness of the initial approximation. This way, the completed convergence analysis is finer and can replace the classical one by Kantorovich and others. A two-point boundary value problem (TPBVP) is solved to complement this article.

Suggested Citation

  • Samundra Regmi & Ioannis K. Argyros & Santhosh George & Michael I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1839-:d:825424
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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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