Let B be a Douglas algebra and let B be the algebra on the disk generated by the harmonic extensions of the functions in B. In this paper we show that B is generated by H∞(D) and the complex conjugates of the harmonic extensions of the interpolating Blaschke products invertible in B. Every element S in the Toeplitz algebra TB generated by Toeplitz operators (on the Bergman space) with symbols i...

We consider the estimation of the spectral density matrix of a periodically correlated (PC) time series (also known as cyclostationary time series). We use the well known relation between the spectral density matrix of a periodically correlated time series and a stationary vector time series (Gladyshev, 1961). The spectral matrix of the stationary vector time series is estimated using the eigen...

All-pass filter design can be generally achieved by solving a system of linear equations.The associatedmatrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition techni...

Performing joint detection in a TD-CDMA system corresponds to the solution of a large system of linear equations, whose matrix exhibits a strong band and Toeplitz structure. Taking advantage of the structure allows a cheap solution by standard algorithms (Cholesky, QR-decomposition). Including decision feedback into the solution process improves the performance of the system. This, however, lea...

A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiago-nal systems that are diicult to solve eeciently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel preex (SPP), is proposed. The SPP algorithm requires less memory ...

A class ξ of algebras of symmetric n × n matrices, related to Toeplitz-plus-Hankel structures and including the well-known algebra H diagonalized by the Hartley transform, is investigated. The algebras of ξ are then exploited in a general displacement decomposition of an arbitrary n× n matrix A. Any algebra of ξ is a 1-space, i.e., it is spanned by n matrices having as first rows the vectors of...

This work attempts to give a uniied treatment of sensitivity issues in problems involving the application of-orthogonal transformations. Algorithms for such problems are sometimes implemented with minor variations in the way elementary hyperbolic transformations are used to construct a-orthogonal transformation. This results in a possible variation in the condition of the elementary transformat...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

The computation of themodel parameters of a Canonical Polyadic Decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems involving tensor decompositions such as signal proces...

In this paper we present two versions of a parallel algorithm to solve the block–Toeplitz least-squares problem on distributed-memory architectures. We derive a parallel algorithm based on the seminormal equations arising from the triangular decomposition of the product T TT . Our parallel algorithm exploits the displacement structure of the Toeplitz-likematrices using theGeneralized SchurAlgor...