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Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense
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SYSNO ASEP 0467970 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense Author(s) Hnětynková, Iveta (UIVT-O) SAI, RID, ORCID
Plešinger, M. (CZ)
Sima, D.M. (DE)Source Title SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 37, č. 3 (2016), s. 861-876Number of pages 16 s. Language eng - English Country US - United States Keywords total least squares (TLS) problem ; multiple right-hand sides ; core problem ; linear approximation problem ; error-in-variables modeling ; orthogonal regression ; classical TLS algorithm Subject RIV BA - General Mathematics R&D Projects GA13-06684S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000386451400003 EID SCOPUS 84990847714 DOI 10.1137/15M1028339 Annotation Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX \approx B with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnětynková, M. Plešinger, and Z. Strakoš, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 917–931]. The total least squares (TLS) serves as an important example of such approximation problem. Solvability of TLS was discussed in the full generality in [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 748–770]. This theoretical study investigates solvability of core problems with multiple right-hand sides in the TLS sense. It is shown that, contrary to the single right-hand side case, a core problem with multiple right-hand sides may not have a TLS solution. Further possible internal structure of core problems is studied. Outputs of the classical TLS algorithm for the original problem AX \approx B and for the core problem within AX \approx B are compared. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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