International Conference on Multivariate Approximation
September 24-27, 2011

Multivariate Subdivision and Wavelets

Subdivision schemes provide methods for generating surfaces or manifolds from discrete data by an iteration procedure which fills in more details in every step. Several recent developments of multivariate subdivision focus on adaptive and nonstationary schemes. Especially, the analysis of convergence based on the joint spectral radius has been extended to nonstationary subdivision. If all coefficients of the subdivision scheme are nonnegative, the close relation to non-stationary Markov processes and extremal norms is a new and promising direction of research.

Methods for data analysis employ the multivariate wavelet and frame transform. The recent developments of Shearlets and Fusion Frames have enlarged the possible range of applications, as certain restrictions related to the intrinsic univariate nature of certain function systems can be removed.