An improved error analysis for Newton-like methods under generalized conditions
type: Item
instance of: scholarly article
title: An improved error analysis for Newton-like methods under generalized conditions
zbMATH Open document ID: 1030.65060
DOI: 10.1016/S0377-0427(03)00390-X
author: Ioannis Konstantinos Argyros
published in: Journal of Computational and Applied Mathematics
publication date: 2003-08-25T00:00:00Z
review text: The author is concerned with the problem of approximating a locally unique solution \(x^*\) of the equation \(F(x)=0\), where \(F\) is a Fréchet-differentiable operator. Using Newton-like methods in a Banach space setting, under new and very general conditions he provides different sufficient convergence conditions than before. After his introducing of more precise majorizing sequences, he obtains finer error estimates and a better information on the location of the solution. His results reduce to earlier ones for special choices of majorizing functions. Finally, as an application, he shows that in the case of Newton's method the famous Newton-Kantorovich hypothesis can be weakened under the same information.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1970736
zbMATH Keywords: Newton-like method
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: Newton-Kantorovich hypothesis
zbMATH Keywords: majorant principle
zbMATH Keywords: majorizing sequence
zbMATH Keywords: radius of convergence
zbMATH Keywords: Banach space
zbMATH Keywords: error estimates
reviewed by: Yu Wenhuan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970736