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Block Factorization of Hankel Matrices and Euclidean Algorithm

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, France Laboratoire 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 in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < n

Keywords

block factorizationHankel matricesToeplitz matricesEuclidean algorithm
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9th International Conference on Numerical Analysis and Optimization , 2010 , pp. 48 - 54
Copyright
© EDP Sciences, 2010

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References

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