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

Author

Listed:
  • Samundra Regmi

    (Learning Commons, University of North Texas at Dallas, Dallas, TX 75201, 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, Mangalore 575025, India)

  • Christopher I. Argyros

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

Abstract

There are a plethora of semi-local convergence results for Newton’s method (NM). These results rely on the Newton–Kantorovich criterion. However, this condition may not be satisfied even in the case of scalar equations. For this reason, we first present a comparative study of established classical and modern results. Moreover, using recurrent functions and at least as small constants or majorant functions, a finer convergence analysis for NM can be provided. The new constants and functions are specializations of earlier ones; hence, no new conditions are required to show convergence of NM. The technique is useful on other iterative methods as well. Numerical examples complement the theoretical results.

Suggested Citation

  • Samundra Regmi & Ioannis K. Argyros & Santhosh George & Christopher I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1225-:d:789631
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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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