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

SYSNO ASEP	0329240
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data
Title	Regularizační efekt Golub-Kahanovy bidiagonalizace a vyjevování hladiny šumu v datech
Author(s)	Hnětynková, Iveta (UIVT-O)_{SAI, RID, ORCID} Plešinger, Martin (UIVT-O)_{RID, SAI, ORCID} Strakoš, Zdeněk (UIVT-O)_{SAI, RID, ORCID}
Source Title	Bit. - : Springer - ISSN 0006-3835 Roč. 49, č. 4 (2009), s. 669-696
Number of pages	28 s.
Language	eng - English
Country	SE - Sweden
Keywords	ill-posed problems ; Golub-Kahan iterative bidiagonalization ; Lanczos tridiagonalization ; noise revealing
Subject RIV	BA - General Mathematics
R&D Projects	IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000271948000002
EID SCOPUS	77949654686
DOI	10.1007/s10543-009-0239-7
Annotation	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.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2010

Number of the records: 1