On solution of total least squares problems with multiple right‐hand sides

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 [2], and S. Van Huffel, J. Vandewalle [4], and then complemented recently by the core problem approach of C.C. Paige, Z. Strakoš [5,6,7]. 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)