Forcing sequences and inexact Newton iterates in Banach space
type: Item
instance of: scholarly article
title: Forcing sequences and inexact Newton iterates in Banach space
zbMATH Open document ID: 0944.65060
DOI: 10.1016/S0893-9659(99)00148-2
author: Ioannis Konstantinos Argyros
published in: Applied Mathematics Letters
publication date: 2000-09-13T00:00:00Z
review text: This paper deals with inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Under an assumption on the second Fréchet-derivative of the operator involved, the author essentially reproduces all results found earlier. In particular, the author shows inexact Newton methods are locally convergent if the forcing sequence is uniformly less than one and shows how to choose a forcing sequence which preserves the rapid convergence of Newton's method. However, the obtained upper error bounds on the distances involved are smaller.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1429493
zbMATH Keywords: inexact Newton method
zbMATH Keywords: Banach space
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: superlinear convergence
zbMATH Keywords: strong convergence
zbMATH Keywords: weak convergence
zbMATH Keywords: error bounds
reviewed by: Karel Najzar
MaRDI profile type: Publication
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full work available at URL: s0893-9659(99)00148-2
OpenAlex ID: W2007108391
Wikidata QID: Q126389045
description: scientific article; zbMATH DE number 1429493