IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1225-d789631.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1225/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/8/1225/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Manoj K. Singh & Ioannis K. Argyros, 2022. "The Dynamics of a Continuous Newton-like Method," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    3. Santhosh George & Jidesh Padikkal & Krishnendu Remesh & Ioannis K. Argyros, 2022. "A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    4. Ioannis K. Argyros & Samundra Regmi & Stepan Shakhno & Halyna Yarmola, 2022. "A Methodology for Obtaining the Different Convergence Orders of Numerical Method under Weaker Conditions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    5. Michael I. Argyros & Ioannis K. Argyros & Samundra Regmi & Santhosh George, 2022. "Generalized Three-Step Numerical Methods for Solving Equations in Banach Spaces," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    6. Janak Raj Sharma & Harmandeep Singh & Ioannis K. Argyros, 2022. "A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    7. 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.
    8. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1225-:d:789631. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.