About: How to make Simpler GMRES and GCR more Stable

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: How to make Simpler GMRES and GCR more Stable Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we analyze the numerical behavior of several minimum residual methods, which are mathematically equivalent to the GMRES method. Two main approaches are compared: the one that computes the approximate solution in terms of a Krylov space basis from an upper triangular linear system for the coordinates, and the one where the approximate solutions are updated with a simple recursion formula. We show that a different choice of the basis can significantly influence the numerical behavior of the resulting implementation. While Simpler GMRES and ORTHODIR are less stable due to the ill-conditioning of the basis used, the residual basis is well-conditioned as long as we have a reasonable residual norm decrease. These results lead to a new implementation, which is conditionally backward stable, and they explain the experimentally observed fact that the GCR method delivers very accurate approximate solutions when it converges fast enough without stagnation. In this paper we analyze the numerical behavior of several minimum residual methods, which are mathematically equivalent to the GMRES method. Two main approaches are compared: the one that computes the approximate solution in terms of a Krylov space basis from an upper triangular linear system for the coordinates, and the one where the approximate solutions are updated with a simple recursion formula. We show that a different choice of the basis can significantly influence the numerical behavior of the resulting implementation. While Simpler GMRES and ORTHODIR are less stable due to the ill-conditioning of the basis used, the residual basis is well-conditioned as long as we have a reasonable residual norm decrease. These results lead to a new implementation, which is conditionally backward stable, and they explain the experimentally observed fact that the GCR method delivers very accurate approximate solutions when it converges fast enough without stagnation. (en)
Title	How to make Simpler GMRES and GCR more Stable How to make Simpler GMRES and GCR more Stable (en)
skos:prefLabel	How to make Simpler GMRES and GCR more Stable How to make Simpler GMRES and GCR more Stable (en)
skos:notation	RIV/67985807:_____/08:00310698!RIV10-MSM-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0554), P(IAA100300802), P(IAA1030405), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Rozložník, Miroslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	370747
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/08:00310698
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	large-scale nonsymmetric linear systems; Krylov subspace methods; minimum residual methods; numerical stability; rounding errors (en)
http://linked.open.../riv/klicoveSlovo	Krylov subspace methods minimum residual methods numerical stability large-scale nonsymmetric linear systems rounding errors
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[39A8983A2584]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Theory of Krylov subspace methods and its relationship to other mathematical disciplines Advanced Remedial Technologies and Processes Development of software system for solving large-scale problems of nonlinear and nonsmooth optimization
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	30
http://linked.open...iv/tvurceVysledku	Rozložník, Miroslav Gutknecht, M. H. Jiránek, P.
http://linked.open...ain/vavai/riv/wos	000263103700013
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	0895-4798
number of pages	17 (xsd:int)
is http://linked.open...avai/riv/vysledek of	How to make Simpler GMRES and GCR more Stable How to make Simpler GMRES and GCR more Stable How to make Simpler GMRES and GCR more Stable How to make Simpler GMRES and GCR more Stable

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 117 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software