About: Numerical stability of orthogonalization methods with a non-standard inner product

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we study the numerical properties of several orthogonalization schemes where the inner product is induced by a nontrivial symmetric and positive definite matrix.We analyze the effect of its conditioning on the factorization and the loss of orthogonality between vectors computed in finite precision arithmetic. We consider the implementation based on the backward stable eigendecomposition, modified and classical Gram–Schmidt algorithms, Gram–Schmidt process with reorthogonalization as well as the implementation motivated by the AINV approximate inverse preconditioner. In this paper we study the numerical properties of several orthogonalization schemes where the inner product is induced by a nontrivial symmetric and positive definite matrix.We analyze the effect of its conditioning on the factorization and the loss of orthogonality between vectors computed in finite precision arithmetic. We consider the implementation based on the backward stable eigendecomposition, modified and classical Gram–Schmidt algorithms, Gram–Schmidt process with reorthogonalization as well as the implementation motivated by the AINV approximate inverse preconditioner. (en)
Title	Numerical stability of orthogonalization methods with a non-standard inner product Numerical stability of orthogonalization methods with a non-standard inner product (en)
skos:prefLabel	Numerical stability of orthogonalization methods with a non-standard inner product Numerical stability of orthogonalization methods with a non-standard inner product (en)
skos:notation	RIV/67985807:_____/12:00376851!RIV13-GA0-67985807
http://linked.open...avai/predkladatel	Ústav informatiky AV ČR, v.v.i.
http://linked.open...avai/riv/aktivita	I P S
http://linked.open...avai/riv/aktivity	I, P(GAP108/11/0853), P(IAA100300802), S
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Tůma, Miroslav 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	155093
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/12:00376851
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	orthogonalization schemes; QR factorization; Gram–Schmidt process; preconditioning; rounding error analysis (en)
http://linked.open.../riv/klicoveSlovo	preconditioning Gram–Schmidt process QR factorization orthogonalization schemes rounding error analysis
http://linked.open...odStatuVydavatele	SE - Švédské království
http://linked.open...ontrolniKodProRIV	[1C47951F8B26]
http://linked.open...i/riv/nazevZdroje	Bit
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Nanostructures with transition metals: Towards ab-initio material design Theory of Krylov subspace methods and its relationship to other mathematical disciplines
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	52
http://linked.open...iv/tvurceVysledku	Kopal, J. Tůma, Miroslav Rozložník, Miroslav Smoktunowicz, A.
http://linked.open...ain/vavai/riv/wos	000310992400011
issn	0006-3835
number of pages	24 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Numerical stability of orthogonalization methods with a non-standard inner product

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