SCHATZMAN , Michelle

International audience

International audience

In this paper, we study the following problem: let $\Omega$ be a half-space of $\mathbb{R}^N$, defined by $\Omega = \{x = (x', x_N) \in\mathbb{R}^/x_N > \}$ where $x' = (x,\ldots, x_{N-1})$ is the usual notation, and let there be given functions $u_0\in H^1(\Omega)$ and $u_1 \in L^2(\Omega)$. We assume that $u_0|_{x_N=0}$ is nonnegative,...

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...

We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and 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...