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Total least squares problem with the arbitrary unitarily invariant norms. (English) Zbl 1367.15017
The author considers the minimization with respect to a general unitarily invariant norm (UIN) for the total least squares (TLS) minimization of an approximation problem \(AX\approx B\) with multiple right-hand sides. Several problems related to TLS with respect to general UIN are studied, in particular the existence and uniqueness condition for solutions and relationship among various TLS solutions.

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F35 Numerical computation of matrix norms, conditioning, scaling
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