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In 1992, Labahn and Shalom showed that the inverse of a Toeplitz matrix can be reconstructed by two of its columns and by some entries of the original Toeplitz matrix. We here present a modification of this result and another (shorter) proof. [Copyright &y& Elsevier]

In this paper, we discuss discrete wavelet transforms for Toeplitz matrices and block–Toeplitz–Toeplitz–block matrices. The main contribution of this paper is to give the Toeplitz-like structure of the wavelet transformed Toeplitz matrices, and show that the computational cost for such structure is O(k3ln) where n is the size of the Toeplitz matrix, k is the order of the wavelet and l is the level used in the wavelet transform. The comparison between the wavelet transformed Toeplitz matrices and the Fourier transformed Toeplitz matrices is also given. [Copyright &y& Elsevier]