The Total Least Squares Problem in AX approximate to B: A New Classification with the Relationship to the Classical Works

0375603 - ÚI 2012 RIV US eng J - Journal Article
Hnětynková, I. - Plešinger, Martin - Sima, D.M. - Strakoš, Z. - Huffel van, S.
The Total Least Squares Problem in AX approximate to B: A New Classification with the Relationship to the Classical Works.
SIAM Journal on Matrix Analysis and Applications. Roč. 32, č. 3 (2011), s. 748-770. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA AV ČR IAA100300802
Grant - others:GA ČR(CZ) GA201/09/0917
Program: GA
Institutional research plan: CEZ:AV0Z10300504
Keywords : total least squares * multiple right-hand sides * linear approximation problems * orthogonally invariant problems * orthogonal regression * errors-in-variables modeling
Subject RIV: BA - General Mathematics
Impact factor: 1.368, year: 2011

This paper revisits the analysis of the total least squares (TLS) problem AX approximate to B with multiple right-hand sides given by Van Huffel and Vandewalle in the monograph, The Total Least Squares Problem: Computational Aspects and Analysis, SIAM, Philadelphia, 1991. The newly proposed classification is based on properties of the singular value decomposition of the extended matrix [B|A]. It aims at identifying the cases when a TLS solution does or does not exist and when the output computed by the classical TLS algorithm, given by Van Huffel and Vandewalle, is actually a TLS solution. The presented results on existence and uniqueness of the TLS solution reveal subtleties that were not captured in the known literature.
Permanent Link: http://hdl.handle.net/11104/0208210