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SUMMARY:Polynomial approximation via compressed sensing of high-dimensiona
 l functions on lower sets - Clayton Webster (University of Tennessee\; Oak
  Ridge National Laboratory)
DTSTART:20190219T134000Z
DTEND:20190219T141500Z
UID:TALK120022@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:This talk will focus on compressed sensing approaches to spars
 e polynomial approximation of complex functions in high dimensions. Of par
 ticular interest is the parameterized PDE setting\, where the target funct
 ion is smooth\, characterized by a rapidly decaying orthonormal expansion\
 , whose most important terms are captured by a lower (or downward closed) 
 set. By exploiting this fact\, we will present and analyze several procedu
 res for exactly reconstructing a set of (jointly) sparse vectors\, from in
 complete measurements.&nbsp\; These include novel weighted $\\ell_1$ minim
 ization\, improved iterative hard thresholding\, mixed convex relaxations\
 , as well as nonconvex penalties. Theoretical recovery guarantees will als
 o be presented based on improved bounds for the restricted isometry proper
 ty\, as well as unified null space properties that encompass&nbsp\;all cur
 rently proposed nonconvex minimizations.&nbsp\; Numerical examples are pro
 vided to support the theoretical results and demonstrate the computational
  efficiency of the described compressed sensing methods.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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