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The Core Problem within a Linear Approximation Problem $AX/approx B$ with Multiple Right-Hand Sides
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SYSNO ASEP 0426569 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Core Problem within a Linear Approximation Problem $AX/approx B$ with Multiple Right-Hand Sides Author(s) Hnětynková, Iveta (UIVT-O) SAI, RID, ORCID
Plešinger, Martin (UIVT-O) RID, SAI, ORCID
Strakoš, Z. (CZ)Source Title SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 34, č. 3 (2013), s. 917-931Number of pages 15 s. Language eng - English Country US - United States Keywords total least squares problem ; multiple right-hand sides ; core problem ; linear approximation problem ; error-in-variables modeling ; orthogonal regression ; singular value decomposition Subject RIV BA - General Mathematics R&D Projects GA13-06684S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000325092700004 EID SCOPUS 84887388529 DOI 10.1137/120884237 Annotation This paper focuses on total least squares (TLS) problems $AX/approx B$ with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32, 2011, pp. 748--770]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861--875] showed how necessary and sufficient information for solving $Ax/approx b$ can be revealed from the original data through the so-called core problem concept. In this paper we present a theoretical study extending this concept to problems with multiple right-hand sides. The data reduction we present here is based on the singular value decomposition of the system matrix $A$. We show minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side case. Some other properties of the core problem, however, cannot be extended to the case of multiple right-hand sides. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2014
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