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arXiv · 1401.6341

Hölder Regularity of Geometric Subdivision Schemes

T. Ewald·U. Reif·M. Sabin
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Abstract

We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,α}$-regularity for arbitrary schemes of this type, and $C^{2,α}$-regularity for an important subset thereof, which includes all real-valued schemes. Our results are constructive in the sense that they can be verified explicitly for any scheme and any given set of initial data by a universal procedure. This procedure can be executed automatically and rigorously by a computer when using interval arithmetics.

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T. Ewald, U. Reif, M. Sabin. 2014-01-24. Hölder Regularity of Geometric Subdivision Schemes. https://arxiv.org/abs/1401.6341

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