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...

In MEG source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account. Since this covariance is in general too large to estimate based on the data and to invert efficiently, different parametrizations have been proposed in the literature. These models can be seen as special cases of the gene...

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...

A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with Empirical Mode Decomposition (EMD) and more rigorous mathematical structure, which makes feasible to study convergence compared EMD, ALIF really good potentiality become a reference analysis of signals containing strong co...

In this paper, we survey some of latest developments in using preconditioned conjugate gradient methods for solving mildly ill-conditioned Toeplitz systems where the condition numbers of the systems grow like O(n) for some > 0. This corresponds to Toeplitz matrices generated by functions having zeros of order. Because of the ill-conditioning, the number of iterations required for convergence in...

For a Toeplitz or Toeplitz-like matrix T, we define a preconditioning applied to the symmetrized matrix TnT, which decreases the condition number compared to the one of TnT and even the one of T. This enables us to accelerate the conjugate gradient algorithm for solving Toepiltz and Toeplitz-like linear systems, thus extending the previous results of [1], restricted to the Hermitian positive de...