SOLVABILITY OF THE CORE PROBLEM WITH MULTIPLE RIGHT-HAND SIDES IN THE TLS SENSE

• ID: 2728, RIV: 10331352
• ISSN: 0895-4798, ISBN: not specified
• source: SIAM Journal on Matrix Analysis and Applications
• keywords: total least squares (TLS) problem; multiple right-hand sides; core problem; linear approximation problem; error-in-variables modeling; orthogonal regression; classical TLS algorithm
• authors: Iveta Hnětynková, Martin Plesinger, Diana Maria Sima
• authors from KNM: Hnětynková Iveta

Abstract

Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX approximate to B with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnetynkova, M. Plesinger, and Z. Strakos, 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. Hnetynkova 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 approximate to B and for the core problem within AX approximate to B are compared.