Hermite Subdivision Schemes and Taylor Polynomials

Serge Dubuc (1) , Jean-Louis Merrien (2)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 IRMAR - Institut de Recherche Mathématique de Rennes

We propose a general study of the convergence of a Hermite subdivision scheme $\mathcal H$ of degree $d>0$ in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme $\cal S$. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of $\mathcal S$ is contractive, then $\mathcal S$ is $C^0$ and $\mathcal H$ is $C^d$. We apply this result to two families of Hermite subdivision schemes, the first one is interpolatory, the second one is a kind of corner cutting, both of them use Obreshkov interpolation polynomial.

Mots clés: Subdivision; Hermite schemes; Vector schemes; Convergence

Domaines: Analyse numérique [math.NA]

Serge Dubuc, Jean-Louis Merrien. Hermite Subdivision Schemes and Taylor Polynomials. Constructive Approximation, 2009, 29 (2), pp.219-245. ⟨10.1007/s00365-008-9011-5⟩. ⟨hal-00133615⟩