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The Regularizing Effect of the Golub-Kahan Iterative Bidiagonalization and Revealing the Noise Level in the Data
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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, ORCIDSource Title Bit. - : Springer - ISSN 0006-3835
Roč. 49, č. 4 (2009), s. 669-696Number 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 https://doi.org/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
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