Dual Hermite subdivision schemes of de Rham-type

Costanza Conti (1) , Jean-Louis Merrien (2) , Lucia Romani (3)

1 Dipartimento di Ingegneria Industriale
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Dipartimento Matematica e Applicazioni, Università Milano-Bicocca

Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary and Inherently Non-Stationary Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interpolatory ones, by applying a generalization of the de Rham corner cutting strategy. Exploiting specific tools for the analysis of inherently stationary Hermite subdivision schemes we show that, giving up the interpolation condition, the smoothness of the associated basic limit function can be increased by one, while its support width is only enlarged by one. To accomplish the analysis of de Rham-type Hermite subdivision schemes two new theoretical results are derived and the new notion of HC-convergence is introduced. It allows the construction of Hermite-type subdivision schemes of order d + 1 with the first element of the vector valued limit function having regularity ≥ d.

Mots clés: vector subdivision; Inherently stationary Hermite subdivision; de Rham strategy; dual parametrization; convergence and smoothness analysis

Domaines: Analyse numérique [math.NA]

Costanza Conti, Jean-Louis Merrien, Lucia Romani. Dual Hermite subdivision schemes of de Rham-type. BIT Numerical Mathematics, 2014, 54 (4), pp.955-977. ⟨10.1007/s10543-014-0495-z⟩. ⟨hal-01245720⟩