<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this paper is to investigate the local convergence of the Modified Newton method, i.e. the classical Newton method in which the first derivative is re-evaluated periodically after <italic>m</italic> steps. The convergence order is shown to be <italic>m</italic> + 1. A new algorithm is proposed for the estimation the convergence radius of the method. We propose also a threshold for the number of steps after which is recommended to re-evaluate the first derivative in the Modified Newton method.</p></abstract>

The aim of this paper is to investigate the local convergence of the Modified Newton method, i.e. the classical Newton method in which the first derivative is re-evaluated periodically after m steps. The convergence order is shown to be m + 1. A new algorithm is proposed for the estimation the convergence radius of the method. We propose also a threshold for the number of steps after which is recommended to re-evaluate the first derivative in the Modified Newton method.

On the local convergence of the Modified Newton method

Annals of West University of Timisoara - Mathematics and Computer Science

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

{"article-title":"On the local convergence of the Modified Newton method"}

The aim of this paper is to investigate the local convergence of the Modified Newton method, i.e. the classical Newton method in which the first derivative is...

On the local convergence of the Modified Newton method

Published Online: Dec 08, 2020

Page range: 13 - 22

DOI: https://doi.org/10.2478/awutm-2019-0003

Keywords
modified Newton method, local convergence, radius of convergence

© 2019 Ştefan Măruşter, published by Sciendo

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

On the local convergence of the Modified Newton method

Published Online: Dec 08, 2020

Page range: 13 - 22

DOI: https://doi.org/10.2478/awutm-2019-0003

Keywordsmodified Newton method, local convergence, radius of convergence

© 2019 Ştefan Măruşter, published by Sciendo

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

Keywords
modified Newton method, local convergence, radius of convergence