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Communication Dans Un Congrès Année : 2008

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

Résumé

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.
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Dates et versions

hal-00366292 , version 1 (06-03-2009)

Identifiants

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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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