Browsing by Author "Remesh, K."

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A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations
(MDPI, 2022) George, S.; Padikkal, J.; Remesh, K.; Argyros, I.K.
In this paper, we introduced a new source condition and a new parameter-choice strategy which also gives the known best error estimate. To obtain the results we used the assumptions used in earlier studies. Further, we studied the proposed new parameter-choice strategy and applied it to the method (in the finite-dimensional setting) considered in George and Nair (2017). © 2022 by the authors.
Extending the Applicability of Cordero Type Iterative Method
(MDPI, 2022) Remesh, K.; Argyros, I.K.; Saeed, M.; George, S.; Padikkal, J.
Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero’s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting. © 2022 by the authors.
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.