On the local convergence of the Modified Newton method

Ştefan Măruşter

doi:10.2478/awutm-2019-0003

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On the local convergence of the Modified Newton method

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 57 (2019): Issue 1 (June 2019)

By: Ştefan Măruşter

Open Access

|Dec 2020

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.

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Articles in this issue

DOI: https://doi.org/10.2478/awutm-2019-0003 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 13 - 22

Published on: Dec 8, 2020

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

modified Newton method,

local convergence,

radius of convergence

Related subjects:

Mathematics,

General mathematics

© 2020 Ştefan Măruşter, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 57 (2019): Issue 1 (June 2019)