About: Estimating the backward error in LSQR

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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We propose practical stopping criteria for the iterative solution of sparse linear least squares (LS) problems. Although we focus our discussion on the algorithm LSQR of Paige and Saunders, the ideas discussed here may also be applicable to other algorithms. We review why the 2-norm of the projection of the residual vector onto the range of A is a useful measure of convergence, and we show how this projection can be estimated efficiently at every iteration of LSQR. We also give practical and cheaply computable estimates of the backward error for the LS problem. We propose practical stopping criteria for the iterative solution of sparse linear least squares (LS) problems. Although we focus our discussion on the algorithm LSQR of Paige and Saunders, the ideas discussed here may also be applicable to other algorithms. We review why the 2-norm of the projection of the residual vector onto the range of A is a useful measure of convergence, and we show how this projection can be estimated efficiently at every iteration of LSQR. We also give practical and cheaply computable estimates of the backward error for the LS problem. (en)
Title	Estimating the backward error in LSQR Estimating the backward error in LSQR (en)
skos:prefLabel	Estimating the backward error in LSQR Estimating the backward error in LSQR (en)
skos:notation	RIV/46747885:24220/10:#0001646!RIV11-GA0-24220___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GP201/09/P464)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Jiránek, Pavel
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	Technická univerzita v Liberci / Fakulta mechatroniky, informatiky a mezioborových studií
http://linked.open...dnocenehoVysledku	257541
http://linked.open...ai/riv/idVysledku	RIV/46747885:24220/10:#0001646
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	linear least squares, iterative methods, sparse matrix problems, stopping criteria, backward perturbation analysis, backward error (en)
http://linked.open.../riv/klicoveSlovo	iterative methods stopping criteria backward error backward perturbation analysis linear least squares sparse matrix problems
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[26B1E2049FD6]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Development and analysis of iterative methods for solving large-scale systems of linear algebraic equations in applications
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	31
http://linked.open...iv/tvurceVysledku	Jiránek, Pavel
issn	0895-4798
number of pages	20 (xsd:int)
http://localhost/t...ganizacniJednotka	24220

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