### 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.