Applying standard techniques from Toeplitz operator theory, we analyze the asymptotics of the Hilbert-Smith norms of the TQFT operators coming from isotopy classes of one dimensional oriented submanifolds on a closed oriented surface. We thereby obtain a Toeplitz operator interpretation and generalization of the asymptotic formula obtained recently by Marché and Narimannejad in [MN].

A Newton method to solve total least squares problems for Toeplitz systems of equations is considered. When coupled with a bisection scheme, which is based on an eecient algorithm for factoring Toeplitz matrices, global convergence can be guaranteed. Circulant and approximate factorization preconditioners are proposed to speed convergence when a conjugate gradient method is used to solve linear...

In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deeciency. In this paper, we present an eecient factorization method that exploits symmetry as well as the rank and Toeplitz properties of the given matrix.

Some block Toeplitz methods applied to polynomial matrices are reviewed. We focus on the computation of the structure (rank, null-space, infinite and finite structures) of an arbitrary rectangular polynomial matrix. We also introduce some applications of this structural information in control theory. All the methods outlined here are based on the computation of the null-spaces of suitable block...

In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes “Gohberg–Semencul formula” in the literature. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A09; 65F20

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

Meshless collocation methods based on radial basis functions lead to structured linear systems which, for equispaced grid points, have almost a multilevel Toeplitz structure. In particular, if we consider partial differential equations (PDEs) in two dimensions then we find almost (up to a “low-rank” correction given by the boundary conditions) two-level Toeplitz matrices, i.e., block Toeplitz w...

This paper presents a block Schur algorithm to obtain a factorization of a symmetric block Toeplitz matrix. It is inspired by the various block Schur algorithms that have appeared in the literature but which have not considered the innuence of performance tradeoos on implementation choices. We develop a version based on block hyperbolic Householder reeectors by adapting the representation schem...

In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underlying functions with special zeroes. This shows how to choose the prolongation/restriction operato...