Toeplitz matrices have been found important applications in bioinformatics and computational biology [5-9, 11-12]. In this paper we concern the reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, we first consider the eigenstructure of hermitian Toe...

The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide...

We consider the Toeplitz matrices and obtain their unique LU factor-izations. As by-products, we get an explicit formula for the determinant of a Toeplitz matrix and the application of inversion of Toeplitz matrices .

Transformations of the form A ! C 1 AC 2 are investigated that transform Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices. C 1 and C 2 are matrices related to the discrete Fourier transformation or to various real trigonometric transformations. Combining these results with pivoting techniques,in part II algorithmsfor Toeplitz and Toeplitz-plus-Hankel systems will be p...

We characterize hyponormal “rational” Toeplitz pairs which are pairs of Toeplitz operators whose symbols are rational functions in L∞. The main result of this article is as follows. If T = (Tφ, Tψ) is a hyponormal rational Toeplitz pair then φ− βψ ∈ H for some constant β; in other words, their co-analytic parts necessarily coincide up to a constant multiple. As a corollary we get a complete cha...

A combinatorial proof in terms of Schröder paths and other weighted plane paths is given for a determinant representation of Laurent biorthogonal polynomials (LBPs) and that of coefficients of their three-term recurrence equation. In this process, it is clarified that Toeplitz determinants of the moments of LBPs and their minors can be evaluated by enumerating certain kinds of configurations of...

The preconditioned conjugate gradient (CG) is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit wh...

This paper is concerned with the solution of systems of linear equations ANx = b, where fANg N2N denotes a sequence of positive deenite Hermitian ill{conditioned Toeplitz matrices arising from a (real{valued) nonnegative generating function f 2 C2 with zeros. We construct positive deenite Hermitian preconditioners MN such that the eigenvalues of M ?1 N AN are clustered at 1 and the correspondin...

One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane C is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In [4], the first author obtained a complete description of the commutant of Toeplitz operator T with any quasihomogeneous symbol φ(...

Let Z be a positive hermitian Jordan triple system and B be any connected component of its regular set. A general framework for studying Hardy spaces and associated Toeplitz operators over B is developed. As application , the full spectrum of all Hardy-Toeplitz C-algebras is constructed for the example Z = Sym(2; C), leading to a complete C-structure theory, described in terms of the facial bou...