Extra Regularity of Hermite Subdivision Schemes

Jean-Louis Merrien (1) , Tomas Sauer (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Fakultät für Mathematik und Informatik [Passau]

Hermite subdivision schemes act on vector valued data that is not only considered as functions values of a vector valued function from R to R r , but as evaluations of a function and its consecutive derivatives. Starting with data on r (Z), r = d + 1, interpreted as function value and d = r − 1 consecutive derivatives, we compute successive iterations to define values on r (2 −n Z) and an r-vector valued limit function for whose first component C d-smoothness is generally expected. In this paper, we construct Hermite subdivision schemes such that, beginning with the same data, it is possible to reach a limit function with smoothness d +p for any p > 0. The result is obtained with a generalized Taylor factorization and a smoothness condition for vector subdivision schemes.

Mots clés: Taylor operator; Hermite subdivision; Vector Subdivision; Smoothness

Domaines: Analyse numérique [math.NA]

Jean-Louis Merrien, Tomas Sauer. Extra Regularity of Hermite Subdivision Schemes. Dolomites Research Notes Approximation, 2021, 14 (2), pp.85-94. ⟨hal-03095865⟩