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SUMMARY:Optimal recovery using wavelet trees - Markus Weimar (Ruhr-Univers
 ität Bochum)
DTSTART:20190221T142000Z
DTEND:20190221T145500Z
UID:TALK120202@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:This talk is concerned with the approximation of embeddings be
 tween Besov-type spaces defined on bounded multidimensional domains or (pa
 tchwise smooth) manifolds. We compare the quality of approximations of thr
 ee different strategies based on wavelet expansions. For this purpose\, sh
 arp rates of convergence corresponding to classical uniform refinement\, b
 est $N$-term\, and best $N$-term tree approximation will be presented. In 
 particular\, we will see that whenever the embedding of interest is compac
 t\, greedy tree approximation schemes are as powerful as abstract best $N$
 -term approximation and that (for a large range of parameters) they can ou
 tperform uniform schemes based on a priori fixed (hence non-adaptively cho
 sen) subspaces. This observation justifies the usage of adaptive non-linea
 r algorithms in computational practice\, e.g.\, for the approximate soluti
 on of boundary integral equations arising from physical applications. If t
 ime permits\, implications for the related concept of approximation spaces
  associated to the three approximation strategies will be discussed.
LOCATION:Seminar Room 1\, Newton Institute
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