Abstract
This paper revisits the analysis of the total least squares (TLS) problem AX≈B with multiple right-hand sides given by Van Huffel and Vandewalle in the monograph, The Total Least Squares Problem: Computational Aspects and Analysis, SIAM, Philadelphia, 1991. The newly proposed classification is based on properties of the singular value decomposition of the extended matrix [B|A]. It aims at identifying the cases when a TLS solution does or does not exist and when the output computed by the classical TLS algorithm, given by Van Huffel and Vandewalle, is actually a TLS solution. The presented results on existence and uniqueness of the TLS solution reveal subtleties that were not captured in the known literature.
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