Time: Tuesday, November 17, 2015
3:30pm
MTH3206
Note the new room and time!

Speaker: Wolfgang Dahmen, (RWTH Aachen)

Title: Greedy Algorithms and Thresholding for Dictionaries

Abstract: Redundant systems like frames or even more general dictionaries offer advantages with respect to reducing the effect of transmission errors and, in principle, more flexibility with respect to best n-term approximation. Moreover, they naturally appear in connection with neural networks and kernel based regression methods. On the other hand, the redundancy poses severe obstructions to actually exploiting this flexibility, for instance, when trying to compute best n-term approximations. While thresholding and greedy methods are known to realize best n-term approximation rates for Riesz-bases we analyze and discuss in this talk their performance for more general dictionaries in a Hilbert space. Specifically, we are interested in conditions on the dictionary that allow one to identify approximation classes, i.e., the collection of those elements in the ambient Hilbert space whose best n-term approximation error decays at a given rate, and discuss the somewhat stronger notion of instance optimality. If time permits we indicate some applications to regression or compressed sensing.