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arXiv · 1710.06560

Increasing the smoothness of vector and Hermite subdivision schemes

Caroline Moosmüller·Nira Dyn
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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 $\tfrac{z+1}{2}$. 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).

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Caroline Moosmüller, Nira Dyn. 2017-10-18. Increasing the smoothness of vector and Hermite subdivision schemes. https://doi.org/10.1093/imanum%2Fdry010

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