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

3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), 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.
Keywords :

https://hal.archives-ouvertes.fr/hal-00366292
Contributor : Houssam Khalil <>
Submitted on : Friday, March 6, 2009 - 4:34:56 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:22 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 9:22:02 PM

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### Identifiers

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

### Citation

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

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