Geodesic
Block Factorization of Hankel Matrices and Euclidean Algorithm
S. Belhaj1, 2
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
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 48-54

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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
DOI : 10.1051/mmnp/20105708

S. Belhaj 1, 2

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 
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S. Belhaj. Block Factorization of Hankel Matrices and Euclidean Algorithm. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 48-54. doi: 10.1051/mmnp/20105708

[1] S. Belhaj A fast method to block-diagonalize a Hankel matrix Numer Algor 2008 15 34

[2] S. Belhaj. Block diagonalization of Hankel and Bézout matrices : connection with the Euclidean algorithm, submitted.

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[8] W. B. Gragg, A. Lindquist On partial realization problem Linear Algebra Appl. 1983 277 319

[9] G. Heining, K. Rost. Algebraic methods for Toeplitz-like matrices and operators. Birkhäuser Verlag, Basel, 1984.

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