<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Local convergence analysis of a fourth order method considered by Sharma et. al in [19] for solving systems of nonlinear equations. Using conditions on derivatives upto the order five, they proved that the method is of order four. In this study using conditions only on the first derivative, we prove the convergence of the method in [19]. This way we extended the applicability of the method. Numerical example which do not satisfy earlier conditions but satisfy our conditions are presented in this study.</p></abstract>

Local convergence analysis of a fourth order method considered by Sharma et. al in [19] for solving systems of nonlinear equations. Using conditions on derivatives upto the order five, they proved that the method is of order four. In this study using conditions only on the first derivative, we prove the convergence of the method in [19]. This way we extended the applicability of the method. Numerical example which do not satisfy earlier conditions but satisfy our conditions are presented in this study.

Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

Department of Mathematical and Computational Sciences, National Institute of Technology

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Local convergence analysis of a fourth order method considered by Sharma et. al in [19] for solving systems of nonlinear equations. Using conditions on...

Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

Published Online: Dec 07, 2018

Page range: 23 - 34

Received: Sep 20, 2016

Accepted: Nov 04, 2017

DOI: https://doi.org/10.2478/awutm-2018-0002

Keywords
local convergence, weighted Newton method, Fréchet derivative

© 2018 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

Published Online: Dec 07, 2018

Page range: 23 - 34

Received: Sep 20, 2016

Accepted: Nov 04, 2017

DOI: https://doi.org/10.2478/awutm-2018-0002

Keywordslocal convergence, weighted Newton method, Fréchet derivative

© 2018 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
local convergence, weighted Newton method, Fréchet derivative