About: The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Regularization techniques based on the Golub-Kahan iterative bidiagonalization belong among popular approaches for solving large ill-posed problems. First, the original problem is projected onto a lower dimensional subspace using the bidiagonalization algorithm, which by itself represents a form of regularization by projection. The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied. Stopping criteria for the whole process are then based on the regularization of the projected (small) problem. In this paper we consider an ill-posed problem with a noisy right-hand side (observation vector), where the noise level is unknown. We show how the information from the Golub-Kahan iterative bidiagonalization can be used for estimating the noise level. Such information can be useful for constructing efficient stopping criteria in solving ill-posed problems. Regularization techniques based on the Golub-Kahan iterative bidiagonalization belong among popular approaches for solving large ill-posed problems. First, the original problem is projected onto a lower dimensional subspace using the bidiagonalization algorithm, which by itself represents a form of regularization by projection. The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied. Stopping criteria for the whole process are then based on the regularization of the projected (small) problem. In this paper we consider an ill-posed problem with a noisy right-hand side (observation vector), where the noise level is unknown. We show how the information from the Golub-Kahan iterative bidiagonalization can be used for estimating the noise level. Such information can be useful for constructing efficient stopping criteria in solving ill-posed problems. (en)
Title	The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data (en)
skos:prefLabel	The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data (en)
skos:notation	RIV/67985807:_____/09:00329240!RIV10-AV0-67985807
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(IAA100300802), S, Z(AV0Z10300504), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Strakoš, Zdeněk Hnětynková, Iveta Plešinger, Martin
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	338685
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/09:00329240
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	ill-posed problems; Golub-Kahan iterative bidiagonalization; Lanczos tridiagonalization; noise revealing (en)
http://linked.open.../riv/klicoveSlovo	ill-posed problems Golub-Kahan iterative bidiagonalization Lanczos tridiagonalization noise revealing
http://linked.open...odStatuVydavatele	SE - Švédské království
http://linked.open...ontrolniKodProRIV	[3126C15C89AE]
http://linked.open...i/riv/nazevZdroje	Bit
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (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
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	49
http://linked.open...iv/tvurceVysledku	Strakoš, Zdeněk Plešinger, Martin Hnětynková, Iveta
http://linked.open...ain/vavai/riv/wos	000271948000002
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace Metody moderní matematiky a jejich aplikace
issn	0006-3835
number of pages	28 (xsd:int)
is http://linked.open...avai/riv/vysledek of	The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data

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