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SUMMARY:Optimal Recovery from Data of PDEs with Incomplete Information - P
 eter  Binev (University of South Carolina)
DTSTART:20240715T091500Z
DTEND:20240715T095500Z
UID:TALK218119@talks.cam.ac.uk
DESCRIPTION:\n\n\n\nWe consider the problem of numerically approximating t
 he solutions to a partial differential equation (PDE) when there is insuff
 icient information to determine a unique solution. Our main example is the
  Poisson boundary value problem\, when the boundary data is unknown and in
 stead one observes finitely many linear measurements of the solution. We v
 iew this setting as an optimal recovery problem and develop theory and num
 erical algorithms for its solution. The main vehicle employed is the deriv
 ation and approximation of the Riesz representers of these functionals wit
 h respect to relevant Hilbert spaces of harmonic functions.\n\n\n\n\nThis 
 is a research collaboration with Andrea Bonito\, Albert Cohen\, Wolfgang D
 ahmen\, Ronald DeVore\, and Guergana Petrova.
LOCATION:Seminar Room 1\, Newton Institute
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