A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
type: Item
instance of: scholarly article
title: A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
zbMATH Open document ID: 1057.65029
author: Ioannis Konstantinos Argyros
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: This paper is concerned with the problem of approximating a locally unique solution of the nonlinear equation \( F(x)+G(x) = 0 \), where \(F, G\) are operators defined on a closed ball \(\overline U (w,R)\) centered at point \(w\) and of radius \(R\geq 0\) which is a subset of a Banach space \(X\) with values in Banach space \(Y\). \(F\) is Fréchet-differentiable on \(\overline U (w,R)\), while the differentiability of the operator \(G\) is not assumed. The author provides a local as well as a semilocal convergence analysis for two-point Newton-like methods setting under very general Lipschitz type conditions. Several numerical examples are provided to show that author's results compare favorably with earlier ones.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 2107273
zbMATH Keywords: Banach space
zbMATH Keywords: Newton's method
zbMATH Keywords: majorizing sequence
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: Newton-Kantorovich method
zbMATH Keywords: radius of convergence
zbMATH Keywords: Lipschitz type conditions
zbMATH Keywords: numerical examples
zbMATH Keywords: nonlinear operator equation
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.008
OpenAlex ID: W2067266509
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DOI: 10.1016/J.JMAA.2004.04.008
description: scientific article; zbMATH DE number 2107273