Faculty Publications
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Publications by NITK Faculty
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Item Enlarging the convergence ball of the method of parabola for finding zero of derivatives(Elsevier Inc. usjcs@elsevier.com, 2015) Argyros, I.K.; George, S.We present a new technique for enlarging the convergence ball of the method of parabola in order to approximate a zero of derivatives. This approach also leads to more precise error estimates on the distances involved than in earlier studies such as Hua (1974), Ren and Wu (2009) and Wand (1975). These advantages are obtained under the same computational cost on the Lipschitz constants involved as in the earlier studies. Numerical examples are also given to show the advantages over the earlier work. © 2015 Elsevier Inc. All rights reserved.Item Unified convergence analysis of frozen Newton-like methods under generalized conditions(Elsevier B.V., 2019) Argyros, I.K.; George, S.The objective in this article is to present a unified convergence analysis of frozen Newton-like methods under generalized Lipschitz-type conditions for Banach space valued operators. We also use our new idea of restricted convergence domains, where we find a more precise location, where the iterates lie leading to at least as tight majorizing functions. Consequently, the new convergence criteria are weaker than in earlier works resulting to the expansion of the applicability of these methods. The conditions do not necessarily imply the differentiability of the operator involved. This way our method is suitable for solving equations and systems of equations. Numerical examples complete the presentation of this article. © 2018 Elsevier B.V.Item Convergence analysis for single point Newton-type iterative schemes(Springer, 2020) Argyros, I.K.; George, S.The aim of this article is to present a convergence analysis for single point Newton-type schemes for solving equations with Banach space valued operators. The equations contain a non-differentiable part. Although the convergence conditions are very general, they are weaker than the corresponding ones in earlier works leading to a finer convergence analysis in both the local as well as the semi-local convergence analysis. Therefore, the applicability of these iterative schemes is extended. © 2019, Korean Society for Informatics and Computational Applied Mathematics.