Faculty Publications

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Publications by NITK Faculty

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Author: search.filters.author.George, S.Subject: search.filters.subject.iterative methods

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    A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations
    (MDPI, 2022) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.
    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. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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    Local Convergence of Traub’s Method and Its Extensions
    (MDPI, 2023) Saeed K, M.; Remesh, K.; George, S.; Padikkal, P.; Argyros, I.K.
    In this article, we examine the local convergence analysis of an extension of Newton’s method in a Banach space setting. Traub introduced the method (also known as the Arithmetic-Mean Newton’s Method and Weerakoon and Fernando method) with an order of convergence of three. All the previous works either used higher-order Taylor series expansion or could not derive the desired order of convergence. We studied the local convergence of Traub’s method and two of its modifications and obtained the convergence order for these methods without using Taylor series expansion. The radii of convergence, basins of attraction, comparison of iterations of similar iterative methods, approximate computational order of convergence (ACOC), and a representation of the number of iterations are provided. © 2023 by the authors.