Abstract
This paper establishes an algorithm for the computation of the inverse of a nonsingular, centrosymmetric Toeplitz-plus-Hankel Bezoutian B of order n. The algorithm has O(n 2) computational complexity. In comparison with a previous paper on this topic the main key here is the reduction to the inversion of two symmetric Toeplitz Bezoutians of order n. This approach leads to a simpler algorithm, but it requires an additional assumption in one case. Furthermore, we obtain an explicit representation of B −1 as a sum of a Toeplitz and a Hankel matrix.
Mathematics Subject Classification (2010). Primary 15A09; Secondary 15B05, 65F05.
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Ehrhardt, T., Rost, K. (2017). Fast Inversion of Centrosymmetric Toeplitz-plus-Hankel Bezoutians. In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_14
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DOI: https://doi.org/10.1007/978-3-319-49182-0_14
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-49180-6
Online ISBN: 978-3-319-49182-0
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