<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.</p></abstract>

We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.

Ball convergence for Traub-Steffensen like methods in Banach space

Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Department of Mathematical and Computational Sciences, NIT Karnataka, India-575 025

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Ball convergence for Traub-Steffensen like methods in Banach space"}

We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach...

Ball convergence for Traub-Steffensen like methods in Banach space

Publié en ligne: 09 avr. 2016

Pages: 3 - 16

Reçu: 30 avr. 2015

Accepté: 27 janv. 2016

DOI: https://doi.org/10.1515/awutm-2015-0011

Mots clés
Steffensen method, Traub-Steffensen method, Banach space, Fréchet derivative, local convergence, third order of convergence

© 2015 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Ball convergence for Traub-Steffensen like methods in Banach space

Publié en ligne: 09 avr. 2016

Pages: 3 - 16

Reçu: 30 avr. 2015

Accepté: 27 janv. 2016

DOI: https://doi.org/10.1515/awutm-2015-0011

Mots clésSteffensen method, Traub-Steffensen method, Banach space, Fréchet derivative, local convergence, third order of convergence

© 2015 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Steffensen method, Traub-Steffensen method, Banach space, Fréchet derivative, local convergence, third order of convergence