On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations
type: Item
instance of: scholarly article
title: On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations
zbMATH Open document ID: 1461.65085
author: D. K. R. Babajee
author: Kalyanasundaram Madhu
author: J. Jayaraman
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not require the evaluation of second or higher order Fréchet derivatives and still reaches fourth order convergence. The multi-step version converges with order \(2r+4\), where \(r\) is a positive integer and \(r \geq 1\). We have proved that the root \(\alpha\) is a point of attraction for a general iterative function, whereas the proposed new schemes also satisfy this result. Numerical experiments including an application to 1-D Bratu problem are given to illustrate the efficiency of the new methods. Also, the new methods are compared with some existing methods.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 7042291
zbMATH Keywords: system of nonlinear equation
zbMATH Keywords: Newton's method
zbMATH Keywords: order of convergence
zbMATH Keywords: point of attraction
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a8040895
OpenAlex ID: W1721177227
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DOI: 10.3390/A8040895
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description: scientific article; zbMATH DE number 7042291