On a characterization of some Newton-like methods of \(R\)-order at least three
type: Item
instance of: scholarly article
title: On a characterization of some Newton-like methods of \(R\)-order at least three
zbMATH Open document ID: 1087.65057
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 2005-08-25T00:00:00Z
review text: For the nonlinear equation \(F(x) = 0\) in Banach space an \(R\)-order convergent (\(R\geq 3\)) Newton-like method is introduced with the help of the first and second derivatives. \textit{W. Gander}'s result on Halley's method [Am. Math. Mon. 92, 131--134 (1985; Zbl 0574.65041)] is extended to a Banach space with a multi-parametric family iteration process. The semi-local convergence with \(R\)-order at least three is proven. Numerical examples confirm the order of convergence.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2198614
zbMATH Keywords: Newton method
zbMATH Keywords: nonlinear operator equation \(R\)-order of convergence
zbMATH Keywords: Semilocal convergence
zbMATH Keywords: Banach space
zbMATH Keywords: Halley's method
zbMATH Keywords: numerical examples
reviewed by: Zhen Mei
MaRDI profile type: Publication
full work available at URL: j.cam.2005.01.001
OpenAlex ID: W2035340892
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DOI: 10.1016/J.CAM.2005.01.001
description: scientific article