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Filter Factors of Truncated TLS Regularization with Multiple Observations
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SYSNO ASEP 0474150 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Filter Factors of Truncated TLS Regularization with Multiple Observations Author(s) Hnětynková, I. (CZ)
Plešinger, Martin (UIVT-O) RID, SAI, ORCID
Žáková, J. (CZ)Source Title Applications of Mathematics. - : Springer - ISSN 0862-7940
Roč. 62, č. 2 (2017), s. 105-120Number of pages 16 s. Language eng - English Country CZ - Czech Republic Keywords truncated total least squares ; multiple right-hand sides ; eigenvalues of rank-d update ; ill-posed problem ; regularization ; filter factors Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects GA13-06684S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000400889400002 EID SCOPUS 85015684073 DOI 10.21136/AM.2017.0228-16 Annotation The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems Ax approx b were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of A applied to b. This paper focuses on the situation when multiple observations b1,..., bd are available, i.e., the T-TLS method is applied to the problem AX approx B, where B = [b1,..., bd] is a matrix. It is proved that the filtering representation of the T-TLS solution can be generalized to this case. The corresponding filter factors are explicitly derived. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2018
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