Publication at Faculty of Mathematics and Physics |
2008
Abstract
Consider a linear approximation problem AX~B with multiple right-hand sides. When errors in the data are confirmed both to B and A, the total least squares (TLS) concept is used to solve this problem.
Contrary to the standard least squares approximation problem, a solution of the TLS problem may not exist. For a single (vector) right-hand side, the classical theory has been developed by G.H.
Golub, C.F. Van Loan (1980), and S.
Van Huffel, J. Vandewalle (1991), and then complemented recently by the core problem approach of C.C.
Paige, Z. Strakoš (2002, 2006).
Analysis of the problem with multiple right-hand sides is still under development. In this short contribution we present conditions for the existence of a TLS solution.