1. H\'older Regularity of Geometric Subdivision Schemes
- Author
-
Ewald, T., Reif, U., and Sabin, M.
- Subjects
Mathematics - Metric Geometry ,Mathematics - Classical Analysis and ODEs ,26A16, 68U07 - 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 $C^{1,\alpha}$-regularity for arbitrary schemes of this type, and $C^{2,\alpha}$-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., Comment: 31 pages, 1 figure
- Published
- 2014