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The total least squares problem in $$AX \approx B$$: A new classification with the relationship to the classical works. (English) Zbl 1235.15016
This paper focuses on classification of the total least squares (TLS) formulation of the linear approximation problem with multiple right-hand sides. The newly proposed classification is based on properties of the singular value decomposition of the extended matrix. 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 is actually a TLS solution.

##### MSC:
 15A24 Matrix equations and identities 65F20 Numerical solutions to overdetermined systems, pseudoinverses
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