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Block diagonalization and LU-equivalence of Hankel matrices

✍ Scribed by Nadia Ben Atti; Gema M. Diaz–Toca

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
196 KB
Volume
412
Category
Article
ISSN
0024-3795

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✦ Synopsis

This article presents a new algorithm for obtaining a block diagonalization of Hankel matrices by means of truncated polynomial divisions, such that every block is a lower Hankel matrix. In fact, the algorithm generates a block LU-factorization of the matrix. Two applications of this algorithm are also presented. By the one hand, this algorithm yields an algebraic proof of Frobenius' Theorem, which gives the signature of a real regular Hankel matrix by using the signs of its principal leading minors. On the other hand, the close relationship between Hankel matrices and linearly recurrent sequences leads to a comparison with the Berlekamp-Massey algorithm.

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