Convergence of level-dependent Hermite subdivision schemes

Abstract

Subdivision schemes are known to be useful tools for approximation and interpolation of discrete data. In this paper, we study conditions for the convergence of level-dependent Hermite subdivision schemes, which act on vector valued data interpreting their components as function values and associated consecutive derivatives. In particular, we are interested in schemes preserving spaces of polynomials and exponentials. Such preservation property assures the existence of a cancellation operator in terms of which it is possible to obtain a factorization of the subdivision operators at each level. With the help of this factorization, we provide sufficient conditions for the convergence of the scheme based on some contractivity assumptions on the associated difference scheme.