On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
type: Item
instance of: scholarly article
title: On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
zbMATH Open document ID: 0535.65018
DOI: 10.1016/0024-3795(83)80026-3
author: Kang C. Jea
author: David M. Young
published in: Linear Algebra and its Applications
publication date: 1983-01-01T00:00:00Z
review text: Die Arbeit befaßt sich mit Modifikationen des Verfahrens der konjugierten Gradienten (cg-Verfahren) für nichtsymmetrische Gleichungssysteme \(Ax=b\). Gibt es eine Matrix H mit \(HA=A^ TH\), so lassen sich Modifikationen des cg-Verfahrens mit den von symmetrischen Systemen her bekannten Eigenschaften des Verfahrens angeben. Es wird gezeigt, daß eine solche Matrix H immer existiert, i.a. aber schwer zu bestimmen ist. Geht man zu einem doppelt so großen Blockdiagonalsystem Ã\~x\(=\tilde b\) mit Diagonalblöcken A und \(A^ T\) über, so läßt sich ein entsprechendes \(\tilde H\) leicht finden. Die Formeln für das entsprechende cg-Verfahren werden angegeben und ein Zusammenhang mit der Methode von Lanczos aufgezeigt.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 3850370
zbMATH Keywords: conjugate-gradient methods
zbMATH Keywords: nonsymmetrizable linear systems
zbMATH Keywords: Lanczos method
MaRDI profile type: Publication
full work available at URL: 0024-3795(83)80026-3
OpenAlex ID: W1995020472
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description: scientific article; zbMATH DE number 3850370