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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Polynomial approximation via compressed sensing of
high-dimensional functions on lower sets - Clayto
n Webster (University of Tennessee\; Oak Ridge Nat
ional Laboratory)
DTSTART;TZID=Europe/London:20190219T134000
DTEND;TZID=Europe/London:20190219T141500
UID:TALK120022AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/120022
DESCRIPTION:This talk will focus on compressed sensing approac
hes to sparse polynomial approximation of complex
functions in high dimensions. Of particular intere
st is the parameterized PDE setting\, where the ta
rget function is smooth\, characterized by a rapid
ly decaying orthonormal expansion\, whose most imp
ortant terms are captured by a lower (or downward
closed) set. By exploiting this fact\, we will pre
sent and analyze several procedures for exactly re
constructing a set of (jointly) sparse vectors\, f
rom incomplete measurements. \; These include
novel weighted $\\ell_1$ minimization\, improved i
terative hard thresholding\, mixed convex relaxati
ons\, as well as nonconvex penalties. Theoretical
recovery guarantees will also be presented based o
n improved bounds for the restricted isometry prop
erty\, as well as unified null space properties th
at encompass \;all currently proposed nonconve
x minimizations. \; Numerical examples are pro
vided to support the theoretical results and demon
strate the computational efficiency of the describ
ed compressed sensing methods. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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