<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.</p></abstract>

We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.

Local Convergence and Radius of Convergence for 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 License.

{"article-title":"Local Convergence and Radius of Convergence for Modified Newton Method"}

We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based...

Local Convergence and Radius of Convergence for Modified Newton Method

Published Online: Dec 29, 2017

Page range: 157 - 169

Received: Feb 07, 2017

Accepted: Jul 20, 2017

DOI: https://doi.org/10.1515/awutm-2017-0020

Keywords
Modified Newton method, Local convergence, Local convergence radius

© 2017 Ştefan Măruşter, published by De Gruyter Open

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

Local Convergence and Radius of Convergence for Modified Newton Method

Published Online: Dec 29, 2017

Page range: 157 - 169

Received: Feb 07, 2017

Accepted: Jul 20, 2017

DOI: https://doi.org/10.1515/awutm-2017-0020

KeywordsModified Newton method, Local convergence, Local convergence radius

© 2017 Ştefan Măruşter, published by De Gruyter Open

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

Keywords
Modified Newton method, Local convergence, Local convergence radius