| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 7, 2010
JANO9 – The 9th International Conference on Numerical Analysis and Optimization
|
|
|---|---|---|
| Page(s) | 48 - 54 | |
| DOI | https://doi.org/10.1051/mmnp/20105708 | |
| Published online | 26 August 2010 | |
Block Factorization of Hankel Matrices and Euclidean Algorithm
1
Laboratoire de Mathématiques, CNRS UMR 6623, Université de
Franche-Comté
25030
Besançon cedex,
France
2
Laboratoire LAMSIN, Ecole Nationale d’Ingénieurs de Tunis
BP 37, 1002
Tunis Belvédère,
Tunisie
* Corresponding author: E-mail:
skander.belhaj@univ-fcomte.fr
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
Mathematics Subject Classification: 15A23 / 15B05 / 65F05 / 11C08
Key words: block factorization / Hankel matrices / Toeplitz matrices / Euclidean algorithm
© EDP Sciences, 2010
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