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

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

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