In order to estimate the condition number of the preconditioned matrix proposed in [F.R. Lin, W.K. Ching, Inverse Toeplitz preconditioners for Hermitian Toeplitz systems, Numer. Linear Algebra Appl. 12 (2005) 221–229], we study the inverse of band triangular Toeplitz matrix. We derive an explicit formula for the entries of the inverse of band lower triangular Toeplitz matrix by means of divided...

Unlike Toeplitz operators on H, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several e...

We consider Toeplitz operators on Bergman spaces over the bounded symmetric domain SU(n, n)/S(U(n)×U(n)). As a special case of a previous result, it was shown that Toeplitz operators with radial symbols (that is, symbols that are invariant under the action of S(U(n)×U(n))) generate a commutative C∗-algebra. As a consequence, it is possible to simultaneously diagonalize all Toeplitz operators wi...

A list of technical reports, including some abstracts and copies of some full reports may be found at: Object test coverage using finite state machines. September 1995. On balancing workload in a highly mobile environment. August 1995. Error analysis of a partial pivoting method for structured matrices. June 1995. Abstract In this expository paper, we survey some of the latest developments on u...

In this paper we present two algorithms-one to compute the QR factorization of nearly rank-deecient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely ill-conditioned Toeplitz least-squares problem. The rst algorithm is based on adapting the generalized Schur algorithm to Cauchy-like matrices and has some rank-revealing capability. The other algorithm is ba...

This paper explores the relationship between Toeplitz and circulant matrices. Upper and lower bounds for all eigenvalues of hermitian Toeplitz matrices are given, capitalizing on the possibility of embedding a Toeplitz matrix in a circulant, and of expressing any nn Toeplitz matrix as a sum of two matrices with known eigenvalues. The bounds can be simultaneously found using a single discrete Fo...

It is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered. c © 2007 Elsevier Ltd. All rights reserved.

In this paper we propose an improved MUSIC (Multiple Signal Classification) algorithm applicable for direction of arrival (DOA) estimation of coherent signals in the presence of one-dimensional uniform linear array (ULA), which is based on Toeplitz matrix theory and Fourth-order-cumulants (Foc). In the signal model, a new Toeplitz construction method combining SVD (singular value decomposition)...

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 ...

The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower t...