Computational Analysis Seminar

Andreas Weinmann

(TU Graz)

"Geometric subdivision and interpolatory multiscale transforms for irregular combinatorics"

Date: Mon, November 30, 2009
Time: 14:00
Place: East Hall 2

Abstract: This talk starts with a short introduction to subdivision schemes for meshes which have non-regular combinatorics. We review linear subdivision which handles meshes with vertices in linear spaces, and then explain how a linear rule can be used to define schemes in nonlinear geometries like Riemannian manifolds or Lie groups. We present our results on convergence and smoothness of such geometric rules.

In the second part we define an interpolatory multiscale transformation for functions on a compact 2-manifold with values in a manifold. We characterize the Hölder-Zygmund smoothness of a function between those manifolds in terms of the coeffcient decay w.r.t. this multiscale transform.