In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...

This paper concernes eigenvalue computations with displacement structured matrices, for example, Toeplitz or Toeplitz-plus-Hankel. A technique using isospectral flows is introduced. The flow is enforced to preserve the displacement structure of the originary matrix by means of a suitable constraint added in its formulation. In order to fulfil the constraint, the numerical integration of the flo...

All-pass filter design can be generally achieved by solving a system of linear equations.The associatedmatrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition techni...

A class ξ of algebras of symmetric n × n matrices, related to Toeplitz-plus-Hankel structures and including the well-known algebra H diagonalized by the Hartley transform, is investigated. The algebras of ξ are then exploited in a general displacement decomposition of an arbitrary n× n matrix A. Any algebra of ξ is a 1-space, i.e., it is spanned by n matrices having as first rows the vectors of...

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...