Inexact Newton methods on a vector supercomputer
type: Item
instance of: scholarly article
title: Inexact Newton methods on a vector supercomputer
zbMATH Open document ID: 0839.65068
DOI: 10.1016/0377-0427(94)00002-I
author: Hildegard Foerster
author: Andreas Frommer
author: Günter Mayer
published in: Journal of Computational and Applied Mathematics
publication date: 1996-06-02T00:00:00Z
review text: The authors propose a modification of Newton's method for solving nonlinear systems \(F(x)= 0\), which allows to use the same Jacobian \(F'(x)\) repeatedly and to solve the equations for the correction \(F'(x) \Delta x= -F(x)\) only approximately. Such methods can be useful in cases where the costs for building the Jacobian are high. The authors also point out that forming and solving the equations can parallelize poorly, particularly for problems where the Jacobian is rather sparse. Two lemmas are given to establish local convergence and a theorem is presented that helps to determine the convergence order of this method. Three numerical examples show that the proposed method is able to achieve a much better performance on a vector supercomputer than the exact Newton method.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 804740
zbMATH Keywords: inexact Newton methods
zbMATH Keywords: Jacobian matrix
zbMATH Keywords: nonlinear systems
zbMATH Keywords: local convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: performance
reviewed by: W. Gander
describes a project that uses: NAG
describes a project that uses: nag
MaRDI profile type: Publication
cites work: Q5796557
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full work available at URL: 0377-0427(94)00002-i
OpenAlex ID: W1973392863
Wikidata QID: Q126528045
description: scientific article; zbMATH DE number 804740