We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving lines. We show an explicit connection between the generators of a Toeplitz matrix and the generators of the corresponding module of syzygies. We show that this module is generated by two elements and the solution of ...

The problem we are interested in is the best approximation of a given matrix by a positive semi–definite symmetric Toeplitz matrix. Toeplitz matrices appear naturally in a variety of problems in engineering. Since positive semi–definite Toeplitz matrices can be viewed as shift invariant autocorrelation matrices, considerable attention has been paid to them, especially in the areas of stochastic...

The di erential equation dX dt X k X where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem Starting with the diagonal matrix whose entries are the same as the given eigenvalues the solution ow has been observed numerically to always converge a symmetric Toeplitz matrix as t This paper is an attempt to understand the dynamics involved in...

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hami...

WOJCIECH BULATEK AND JAN KWIATKOWSKI The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z2-extensions are described. Such Toeplitz flows are topo~ logically coalescent . If {go,gl, . . .} is a set of all except at least one prime numbers and Io,Il, . . . are positive integers then the direct sum ®°° o Zy ; I ; ® Z can be the topological centralizer of a Toeplit...

Condit ions are given for the existence of hamiltonian paths and cycles in the so-called Toeplitz graphs, i.e. simple graphs with a symmetric Toeplitz adjacency matrix.

Toeplitz operators are fundamental and ubiquitous in signal processing and information theory as models for linear, time-invariant (LTI) systems. Due to the fact that any practical system can access only signals of finite duration, time-limited restrictions of Toeplitz operators are naturally of interest. To provide a unifying treatment of such systems working on different signal domains, we co...

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant kernel. In this case it is not obvious how to take advantage of t...

We investigate the symmetry resolution of entanglement in presence long-range couplings. To this end, we study symmetry-resolved entropy ground state a fermionic chain that has dimerised hoppings with power-like decaying amplitude -- generalisation Su-Schrieffer-Heeger model. This is system preserves number particles. The each sector calculated via charged moments reduced density matrix. exploi...

We calculate exactly cumulant generating functions (full counting statistics) for the transverse, staggered magnetization, and domain walls at zero temperature a finite interval of $XY$ spin chain. In particular, we also derive universal interpolation formula in scaling limit full statistics transverse magnetization which is based on solution Painlev\'e V equation. By further determining sublea...