Increasing the smoothness of vector and Hermite subdivision schemes

Abstract

In this paper we suggest a method for transforming a vector subdivision scheme generating $C^{\ell }$ limits to another such scheme of the same dimension, generating $C^{\ell +1}$ limits. In scalar subdivision, it is well known that a scheme generating $C^{\ell }$ limit curves can be transformed to a new scheme producing $C^{\ell +1}$ limit curves by multiplying the scheme's symbol with the smoothing factor $\frac{z+1}{2}$. We extend this approach to vector and Hermite subdivision schemes, by manipulating symbols. The algorithms presented in this paper allow to construct vector (Hermite) subdivision schemes of arbitrarily high regularity from a convergent vector scheme (from a Hermite scheme whose Taylor scheme is convergent with limit functions of vanishing first component).

28 pages, 4 figures. Corrected typos, updated contact information

Cited by in corpus (4)

• Analysis and convergence of Hermite subdivision schemes
• Multivariate Generalized Hermite Subdivision Schemes
• A note on spectral properties of Hermite subdivision operators
• Polynomial overreproduction by Hermite subdivision operators, and $p$-Cauchy numbers