1. Journal Articles
Permanent URI for this collectionhttps://idr.nitk.ac.in/handle/1/6
Browse
23 results
Search Results
Item Unified ball convergence of third and fourth convergence order algorithms under ω−continuity conditions(2021) Argyros G.; Argyros M.; Argyros I.K.; George S.There is a plethora of third and fourth convergence order algorithms for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or uniqueness of the solution results if given at all are also based on the existence of high order derivatives. But these problems limit the applicability of the algorithms. That is why we address all these problems under conditions only on the first derivative that appear in these algorithms. Our analysis includes computable error estimations as well as uniqueness results based on ω− continuity conditions on the Fréchet derivative of the operator involved. © 2021 University of Guilan.Item On the solution of equations by extended discretization(2020) Argyros G.I.; Argyros M.I.; Regmi S.; Argyros I.K.; George S.The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found. That is why we present results using ω- continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize ω- continuity our new results improve those in the literature too in the case of Lipschitz or Hölder continuity. Our analysis includes tighter upper error bounds on the distances involved. © 2020 by the authors.Item Newton–Kantorovich regularization method for nonlinear ill-posed equations involving m- accretive operators in Banach spaces(2020) Sreedeep C.D.; George S.; Argyros I.K.In this paper, we study nonlinear ill-posed problems involving m- accretive mappings in Banach spaces. We consider Newton–Kantorovich regularization method for the implementation of Lavrentiev regularization method. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter. © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.Item Local comparison between two ninth convergence order algorithms for equations(2020) Regmi S.; Argyros I.K.; George S.A local convergence comparison is presented between two ninth order algorithms for solving nonlinear equations. In earlier studies derivatives not appearing on the algorithms up to the 10th order were utilized to show convergence. Moreover, no error estimates, radius of convergence or results on the uniqueness of the solution that can be computed were given. The novelty of our study is that we address all these concerns by using only the first derivative which actually appears on these algorithms. That is how to extend the applicability of these algorithms. Our technique provides a direct comparison between these algorithms under the same set of convergence criteria. This technique can be used on other algorithms. Numerical experiments are utilized to test the convergence criteria. © 2020 by the authors.Item Extending the applicability of an Ulm-Newton-like method under generalized conditions in Banach space(2020) Argyros I.K.; George S.The aim of this paper is to extend the applicability of an Ulm-Newton-like method for approximating a solution of a nonlinear equation in a Banach space setting. The sufficient local convergence conditions are weaker than those in the earlier works leading to a larger radius of convergence and more precise error estimations on the distances involved. Numerical examples are also provided. © 2020 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.Item Extended Convergence Of A Two-Step-Secant-Type Method Under A Restricted Convergence Domain(2021) Argyros I.K.; George S.We present a local as well as a semi-local convergence analysis of a two-step secant-type method for solving nonlinear equations involving Banach space valued operators. By using weakened Lipschitz and center Lipschitz conditions in combination with a more precise domain containing the iterates, we obtain tighter Lipschitz constants than in earlier studies. This technique lead to an extended convergence domain, more precise information on the location of the solution and tighter error bounds on the distances involved. These advantages are obtained under the same computational effort, since the new constants are special cases of the old ones used in earlier studies. The new technique can be used on other iterative methods. The numerical examples further illustrate the theoretical results. © 2021, Kragujevac Journal of Mathematics. All Rights Reserved.Item Direct comparison between two third convergence order schemes for solving equations(2020) Regmi S.; Argyros I.K.; George S.We provide a comparison between two schemes for solving equations on Banach space. A comparison between same convergence order schemes has been given using numerical examples which can go in favor of either scheme. However, we do not know in advance and under the same set of conditions which scheme has the largest ball of convergence, tighter error bounds or best information on the location of the solution. We present a technique that allows us to achieve this objective. Numerical examples are also given to further justify the theoretical results. Our technique can be used to compare other schemes of the same convergence order. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Item Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative(2021) George S.; Argyros I.K.; Jidesh P.; Mahapatra M.; Saeed M.Using conditions on the second Fréchet derivative, fifth order of convergence was established in Singh et al. (Mediterr J Math 13:4219–4235, 2016) for an iterative method. In this paper, we establish fifth order of convergence of the method using assumptions only on the first Fréchet derivative of the involved operator. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.Item Convergence analysis of some iterative methods using tangential-like conditions(2020) Argyros I.K.; George S.We introduce tangential-like conditions which in general are weaker than the usual Lipschitz-like conditions in order to show the local as well as the semi-local convergence of some iterative methods approximating solutions of nonlinear equations in Banach space. Numerical examples further validate the theoretical results showing that equations can be solved with the new conditions but not with the old ones. © 2020, International Publications. All rights reserved.Item COMPARISON BETWEEN SOME SIXTH CONVERGENCE ORDER SOLVERS UNDER THE SAME SET OF CRITERIA(2020) Argyros I.K.; George S.Different set of criteria based on the seventh derivative are used for convergence of sixth order methods. Then, these methods are compared using numerical examples. But we do not know: if the results of those comparisons are true if the examples change; the largest radii of convergence; error estimates on distance between the iterate and solution, and uniqueness results that are computable. We address these concerns using only the first derivative and a common set of criteria. Numerical experiments are used to test the convergence criteria and further validate the theoretical results. Our technique can be used to make comparisons between other methods of the same order. © Petrozavodsk State University, 2020
- «
- 1 (current)
- 2
- 3
- »