On inversion of Toeplitz and close to Toeplitz matrices (Q1071845)

The authors prove that just three properly chosen columns of the inverse of a Toeplitz matrix T suffice in every case to determine the whole of \(T^{-1}\). This generalizes earlier results involving two columns, of \textit{I. C. Gohberg} and \textit{A. A. Semencul} [Mat. Issled. 7, No.2(24), 201-223 (1972; Zbl 0288.15004)] and of \textit{I. C. Gohberg} and \textit{N. Ya. Krupnik} [ibid. 7, No.2(24), 272-283 (1972; Zbl 0288.15005)]. These authors also proved some socalled invertibility theorems which are generalized in this paper. In the last section the same principle is applied to some non-Toeplitz matrices.