Third-order modifications of Newton's method based on Stolarsky and Gini means
type: Item
instance of: scholarly article
title: Third-order modifications of Newton's method based on Stolarsky and Gini means
zbMATH Open document ID: 1277.65034
published in: Journal of Computational and Applied Mathematics
publication date: 2013-04-22T00:00:00Z
review text: The authors consider modifications of some third-order variants of the classical Newton's method, namely \(x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}\phi(s(x_n))\), where \(s(x)=\frac{f'(x-\frac{f(x)}{f'(x)})}{f'(x)}\). They approximate \(f'(x_n)\) by the Stolarsky mean [\textit{K. B. Stolarsky}, Am. Math. Mon. 87, 545--548 (1980; Zbl 0455.26008)] and the Gini mean [\textit{K. B. Stolarsky}, Math. Mag. 48, 87--92 (1975; Zbl 0302.26003)], respectively. They prove third-order convergence of such modified Newton's methods. The results of numerical experiments show that their methods produce better results than several well-known algorithms.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 6156305
zbMATH Keywords: nonlinear equation
zbMATH Keywords: Newton's method
zbMATH Keywords: third-order method
zbMATH Keywords: Gini mean
zbMATH Keywords: Stolarsky mean
zbMATH Keywords: numerical experiments
zbMATH Keywords: algorithm
author: Djordje Herceg
author: Dragoslav Herceg
reviewed by: Przemysław Stpiczyński
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: j.cam.2012.12.008
OpenAlex ID: W1974194877
DOI: 10.1016/J.CAM.2012.12.008
description: scientific article; zbMATH DE number 6156305