<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.</p></abstract>

The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.

Local convergence comparison between two novel sixth order methods for solving equations

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving...

Local convergence comparison between two novel sixth order methods for solving equations

Published Online: Dec 05, 2019

Page range: 5 - 19

Received: Apr 07, 2018

Accepted: Jul 07, 2018

DOI: https://doi.org/10.2478/aupcsm-2019-0001

Keywords
Jarratt-like method, sixth order of convergence, local convergence, Banach space, Fréchet-derivative

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Local convergence comparison between two novel sixth order methods for solving equations

Published Online: Dec 05, 2019

Page range: 5 - 19

Received: Apr 07, 2018

Accepted: Jul 07, 2018

DOI: https://doi.org/10.2478/aupcsm-2019-0001

KeywordsJarratt-like method, sixth order of convergence, local convergence, Banach space, Fréchet-derivative

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Keywords
Jarratt-like method, sixth order of convergence, local convergence, Banach space, Fréchet-derivative