T. Ehrhardt, K. Rost: Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians

Author(s):

T. Ehrhardt
K. Rost

Title:

T. Ehrhardt, K. Rost: Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2014

Mathematics Subject Classification:

    15A09 []
    15B05 []
    65F05 []

Abstract:

In this paper we compute the inverse of a nonsingular, centro\-skew\-symmetric Toeplitz-plus-Hankel Bezoutian $B$ of (even) order $n$ and find a representation of $B^{-1}$ as a sum of a Toeplitz and a Hankel matrix. Two possibilities are discussed. In the first one, the problem is reduced to the inversion of two skewsymmetric Toeplitz Bezoutians of order $n$. In the second one, the problem is tackled via the inversion of two Hankel Bezoutians of half the order $\frac{n}{2}$. The inversion of Toeplitz or Hankel Bezoutians was the subject of a previous paper. Both approaches lead to fast $O(n^2)$ inversion algorithms.

Keywords:

Bezoutian matrix, Toeplitz matrix, Hankel matrix, Toeplitz-plus-Hankel matrix, matrix inversion

Language:

English

Publication time:

07/2014