On the behaviour of approximate Newton methods
type: Item
instance of: scholarly article
title: On the behaviour of approximate Newton methods
zbMATH Open document ID: 0579.65056
DOI: 10.1007/BF02252511
author: Igor Moret
published in: Computing
publication date: 1986-01-01T00:00:00Z
review text: When Newton's method is used for solving nonlinear equations in Banach spaces, at each step of the iterative procedure the solution of a linear equation is requested. When these equations are solved approximately we have a so-called approximate Newton method. The paper is devoted to the study of the convergence properties of such iterations, under Kantorovich type assumptions. Some criteria are given in order to control their convergence and speed of convergence. Moreover, some a posteriori error estimates are proposed. The general results are applied, as example, to Newton-iterative methods.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 3928225
zbMATH Keywords: Newton's method
zbMATH Keywords: Banach spaces
zbMATH Keywords: approximate Newton method
zbMATH Keywords: speed of convergence
zbMATH Keywords: a posteriori error estimates
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02252511
OpenAlex ID: W355496366
description: scientific article; zbMATH DE number 3928225