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.

In this paper, we present several high performance variants of the classical Schur algorithm to factor various Toeplitz matrices. For positive definite block Toeplitz matrices, we show how hyperbolic Householder transformations may be blocked to yield a block Schur algorithm. This algorithm uses BLAS3 primitives and makes efficient use of a memory hierarchy. We present three algorithms for inde...

With the change of variables U = U*q, substitution into (21) results in UCU*q = Ud. Consequently, the solution vector U of (20) can be obtained from the solution vector q of (22) or q can be obtained from U. Note that if a system of real equations is Toeplitz-plus-Hankel (T + H) , where T i s symmetric Toeplitz and H i s skew-centrosym-metric Hankel, then the equations may be transformed into H...

A recent linear time-varying (LTV) generalisation of Vinnicombe’s ν-gap measure of the difference between openloop systems from a closed-loop perspective, is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parametrised by start time. It is shown that the LTV definition of the ν-gap is invariant...

A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

A fast approximate inversion algorithm is proposed for two-level Toeplitz matrices (block Toeplitz matrices with Toeplitz blocks). It applies to matrices that can be sufficiently accurately approximated by matrices of low Kronecker rank and involves a new class of tensor-displacement-rank structured (TDS) matrices. The complexity depends on the prescribed accuracy and typically is o(n) for matr...

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid...

We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...