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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:info@newton.ac.uk
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