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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Optimal recovery using wavelet trees - Markus Weim
 ar (Ruhr-Universität Bochum)
DTSTART;TZID=Europe/London:20190221T142000
DTEND;TZID=Europe/London:20190221T145500
UID:TALK120202AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/120202
DESCRIPTION:This talk is concerned with the approximation of e
 mbeddings between Besov-type spaces defined on bou
 nded multidimensional domains or (patchwise smooth
 ) manifolds. We compare the quality of approximati
 ons of three different strategies based on wavelet
  expansions. For this purpose\, sharp rates of con
 vergence corresponding to classical uniform refine
 ment\, best $N$-term\, and best $N$-term tree appr
 oximation will be presented. In particular\, we wi
 ll see that whenever the embedding of interest is 
 compact\, greedy tree approximation schemes are as
  powerful as abstract best $N$-term approximation 
 and that (for a large range of parameters) they ca
 n outperform uniform schemes based on a priori fix
 ed (hence non-adaptively chosen) subspaces. This o
 bservation justifies the usage of adaptive non-lin
 ear algorithms in computational practice\, e.g.\, 
 for the approximate solution of boundary integral 
 equations arising from physical applications. If t
 ime permits\, implications for the related concept
  of approximation spaces associated to the three a
 pproximation strategies will be discussed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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