Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials.

Houssam Khalil 1, 2, 3 Bernard Mourrain 3 Michelle Schatzman 1, 2
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this paper, we re-investigate the resolution of Toeplitz systems $T\, u =g$, from a new point of view, by correlating the solution of such problems with syzygies of polynomials or moving lines. We show an explicit connection between the generators of a Toeplitz matrix and the generators of the corresponding module of syzygies. We show that this module is generated by two elements of degree $n$ and the solution of $T\,u=g$ can be reinterpreted as the remainder of an explicit vector depending on $g$, by these two generators.
Type de document :
Communication dans un congrès
Vadim Olshevsky & Eugene Tyrtyshnikov. international seminar matrix methods and operator equations (MM&OE), Jul 2007, Moscou, Russia. pp.296-312, 2008
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https://hal.archives-ouvertes.fr/hal-00366292
Contributeur : Houssam Khalil <>
Soumis le : vendredi 6 mars 2009 - 16:34:56
Dernière modification le : vendredi 26 octobre 2018 - 10:45:47
Document(s) archivé(s) le : mardi 8 juin 2010 - 21:22:02

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  • HAL Id : hal-00366292, version 1
  • ARXIV : 0903.1244

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Houssam Khalil, Bernard Mourrain, Michelle Schatzman. Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials.. Vadim Olshevsky & Eugene Tyrtyshnikov. international seminar matrix methods and operator equations (MM&OE), Jul 2007, Moscou, Russia. pp.296-312, 2008. 〈hal-00366292〉

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