Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

0467970 - ÚI 2017 RIV US eng J - Journal Article
Hnětynková, Iveta - Plešinger, M. - Sima, D.M.
Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense.
SIAM Journal on Matrix Analysis and Applications. Roč. 37, č. 3 (2016), s. 861-876. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
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
Impact factor: 2.194, year: 2016

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.
Permanent Link: http://hdl.handle.net/11104/0265909