Faculty Publications

Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736

Publications by NITK Faculty

Browse

Author: search.filters.author.Kunnarath, A.Subject: search.filters.subject.Fréchet derivative

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    On the Order of Convergence and the Dynamics of Werner-King’s Method
    (Universal Wiser Publisher, 2023) George, S.; Argyros, I.K.; Kunnarath, A.; Padikkal, P.
    In this paper, we present the local convergence analysis of Werner-King’s method to approximate the solution of a nonlinear equation in Banach spaces. We establish the local convergence theorem under conditions on the first and second Fréchet derivatives of the operator involved. The convergence analysis is not based on the Taylor expansions as in the earlier studies (which require the assumptions on the third order Fréchet derivative of the operator involved). Thus our analysis extends the applicability of Werner-King’s method. We illustrate our results with numerical examples. Moreover, the dynamics and the basins of attraction are developed and demonstrated. © 2023 Santhosh George, et al.
  • No Thumbnail Available
    Item
    On the convergence of open Newton’s method
    (Springer Science and Business Media B.V., 2023) Kunnarath, A.; George, S.; Sadananda, R.; Padikkal, J.; Argyros, I.K.
    Cordero and Torregrosa proved the convergence of two Newton’s-like methods in 2007. Using Taylor expansion (requiring existence of derivatives of order up to four of the involved operator) they obtained the convergence order three for these methods. The convergence order three is obtained for Open Newton’s method and two extensions of it with assumptions only on first two derivatives of the operator involved. We verified the results with examples and dynamics of the results are presented. © 2023, The Author(s), under exclusive licence to The Forum D’Analystes.
  • No Thumbnail Available
    Item
    Convergence Order of a Class of Jarratt-like Methods: A New Approach
    (Multidisciplinary Digital Publishing Institute (MDPI), 2025) Kunnarath, A.; George, S.; Padikkal, J.; Argyros, I.K.
    Symmetry and anti-symmetry appear naturally in the study of systems of nonlinear equations resulting from numerous fields. The solutions of such equations can be obtained in analytical form only in some special situations. Therefore, algorithms or iterative schemes are mostly studied, which approximate the solution. In particular, Jarratt-like methods were introduced with convergence order at least six in Euclidean spaces. We study the methods in the Banach-space setting. Semilocal convergence is studied to obtain the ball containing the solution. The local convergence analysis is performed without the help of the Taylor series with relaxed differentiability assumptions. Our assumptions for obtaining the convergence order are independent of the solution; earlier studies used assumptions involving the solution for local convergence analysis. We compare the methods numerically with similar-order methods and also study the dynamics. © 2024 by the authors.