It is well-known from the work of A. Brown and P.R. Halmos that an infinite Toeplitz matrix is normal if and only if it is a rotation and translation of a Hermitian Toeplitz matrix. In the present article we prove that all finite normal Toeplitz matrices are either generalised circulants or are obtained from Hermitian Toeplitz matrices by rotation and translation. ∗Supported in part by an NSERC...

In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can be utilized to reduce the computational complexity from [Formula: see text] to...

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...

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C∗algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C∗-algebras determined by an increasing sequence of positive integers, each divid...

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...

In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.