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Block Factorization of Hankel Matrices and EuclideanAlgorithm

Published online by Cambridge University Press:  26 August 2010

A. Taik and
S. Belhaj
S. Belhaj*
Affiliation:
Laboratoire de Mathématiques, CNRS UMR 6623, Université de Franche-Comté 25030 Besançon cedex, FranceLaboratoire LAMSIN, Ecole Nationale d’Ingénieurs de Tunis BP 37, 1002 Tunis Belvédère, Tunisie
*
*Corresponding author: E-mail:skander.belhaj@univ-fcomte.fr
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Abstract

It is shown that a real Hankel matrix admits an approximate block diagonalization inwhich the successive transformation matrices are upper triangular Toeplitz matrices. Thestructure of this factorization was first fully discussed in [1]. This approach isextended to obtain the quotients and the remainders appearing in the Euclidean algorithmapplied to two polynomials u(x) andv(x) of degree n andm, respectively, whith m <n

Keywords

block factorizationHankel matricesToeplitz matricesEuclidean algorithm

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References

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