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Calcul rapide sur les matrices structurées : Les matrices de Hankel.

Abstract : We give a new algorithm for the blocs diagonalization of Hankel matrices. When the matrix corresponds to a linear recurrent sequence we obtain a simplified version of Berlekamp-Massey's algorithm, more easy to implement and to understand than the usual one. Also our version is slightly faster and allows us to use lazzy techniques. We give a very simple and purely algebraic proof of the frobenius's theorem for the signature of real Hankel matrices. We give a study of the Extended Euclidean Algorithm and of his matricial versions using Hankel or Bezout matrices and we explain the links between all these versions.
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Submitted on : Wednesday, April 28, 2010 - 9:37:25 AM
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  • HAL Id : tel-00477090, version 1


Nadia Ben Atti. Calcul rapide sur les matrices structurées : Les matrices de Hankel.. Mathématiques [math]. Université de Franche-Comté, 2008. Français. ⟨tel-00477090⟩



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