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

Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX ≈ 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 ≈ B and for the core problem within AX ≈ B are compared. [ABSTRACT FROM AUTHOR]