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The solvability of the multidimensional total least perturbation problem in spectral norm. (Chinese. English summary) Zbl 0883.65033
Much attention has been paid to the total least squares problem in Frobenius norm (TLSF) proposed by G. H. Golub and C. F. van Loan [SIAM J. Numer. Anal. 17, 883-893 (1980; Zbl 0468.65011)]. This paper deals with the multidimensional TLS in spectral norm (TLSS). A necessary and sufficient condition for the solvability of this TLS problem is proved. The result obtained in this paper shows that the solvability condition for the TLSS is weaker than that for the TLSF. Obviously, numerical methods for the TLSS need to be studied further.

65F20 Numerical solutions to overdetermined systems, pseudoinverses