Geodesic
Inversion of centrosymmetric Toeplitz-plus-Hankel bezoutians
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 106-135.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we discuss how to compute the inverse of a nonsingular, centrosymmetric Toeplitz-plus-Hankel Bezoutian $B$ of order $n$ and how to find a representation of $B^{-1}$ as a sum of a Toeplitz and a Hankel matrix. Besides the known splitting property of $B$ as a sum of two split-Bezoutians, the connection of the latter to Hankel Bezoutians of about half size is used. The fast inversion of the Hankel Bezoutians together with an inversion formula, which was the subject of a previous paper, leads us to an inversion formula for $B^{-1}$ as a Toeplitz-plus-Hankel matrix. It also enables us to design an $O(n^2)$ inversion algorithm.
Classification : 15A09, 15B05, 65F05
Keywords: Bezoutian matrix, Toeplitz matrix, Hankel matrix, Toeplitz-plus-Hankel matrix, matrix inversion 
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     author = {Ehrhardt, Torsten and Rost, Karla},
     title = {Inversion of centrosymmetric {Toeplitz-plus-Hankel} bezoutians},
     journal = {Electronic transactions on numerical analysis},
     pages = {106--135},
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     volume = {42},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a4/}
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Ehrhardt, Torsten; Rost, Karla. Inversion of centrosymmetric Toeplitz-plus-Hankel bezoutians. Electronic transactions on numerical analysis, Tome 42 (2014), pp. 106-135. http://geodesic.mathdoc.fr/item/ETNA_2014__42__a4/