Faculty Publications

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

Publications by NITK Faculty

Browse

Author: search.filters.author.Sadananda, R.Subject: search.filters.subject.Banach space

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Order of Convergence, Extensions of Newton–Simpson Method for Solving Nonlinear Equations and Their Dynamics
    (MDPI, 2023) George, S.; Kunnarath, A.; Sadananda, R.; Padikkal, J.; Argyros, I.K.
    Local convergence of order three has been established for the Newton–Simpson method (NS), provided that derivatives up to order four exist. However, these derivatives may not exist and the NS can converge. For this reason, we recover the convergence order based only on the first two derivatives. Moreover, the semilocal convergence of NS and some of its extensions not given before is developed. Furthermore, the dynamics are explored for these methods with many illustrations. The study contains examples verifying the theoretical conditions. © 2023 by the authors.
  • 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
    Unified Convergence Analysis of Certain At Least Fifth Order Methods
    (SINUS Association, 2025) Sadananda, R.; Gopal, M.; George, S.; Argyros, I.K.
    A class of iterative methods was developed by Xiao and Yin in 2015 and obtained convergence order five using Taylor expansion. They had imposed the conditions on the derivatives of the involved operator of order at least up to four. In this paper, the order of convergence is achieved by imposing conditions only on the first two derivatives of the operator involved. The assumptions under consideration are weaker and the analysis is done in the more general setting of Banach spaces without using Taylor series expansion. The semi-local convergence analysis is also given. Further, the theory is justified by numerical examples. © 2024, SINUS Association. All rights reserved.