The Bareiss algorithm is one of the classical fast solvers for systems of linear equations with Toeplitz coeecient matrices. The method takes advantage of the special structure, and it computes the solution of a Toeplitz system of order N with only O(N 2) arithmetic operations, instead of O(N 3) operations. However, the original Bareiss algorithm requires that all leading principal sub-matrices...

The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...

In this paper, a property of Schur polynomial of real coe cients and real Toeplitz matrix is given. Suppose that the vector of real coe cients of a Schur polynomial annihilates a real Toeplitz matrix, then the Toeplitz matrix is in fact a zero matrix.

An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.

In this paper we characterize when the product of two block Toeplitz operators is a compact perturbation of a block Toeplitz operator on the Hardy space of the open unit disk. Necessary and suucient conditions are given for the commu-tator of two block Toeplitz operators to be compact.