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SUMMARY:Optimal recovery in the uniform norm - David Krieg (Universität P
 assau)
DTSTART:20240716T103000Z
DTEND:20240716T111000Z
UID:TALK218146@talks.cam.ac.uk
DESCRIPTION:We consider the problem of approximating an unknown bounded fu
 nction f based on a finite number of function values. The function is defi
 ned on an arbitrary set and the error is measured in the uniform norm.\n&n
 bsp\;\nWe show that for any n-dimensional space&nbsp\;Vn of bounded functi
 ons\, the knowledge of 2n function values suffices to compute an approxima
 tion of f within Vn whose error exceeds the error of best approximation of
  f within Vn by a factor of order at most n1/2. Previously\, it was known 
 that n function values can give the optimal approximation up to a factor&n
 bsp\;n and 9n function values can give the optimal approximation up to a c
 onstant factor. The new result counterbalances the oversampling and the er
 ror.\n&nbsp\;\nThe problem is related to the discretization of the uniform
  norm on Vn.\n&nbsp\;\nThis is joint work with Kateryna Pozharska\, Mario 
 Ullrich\, and Tino Ullrich.
LOCATION:Seminar Room 1\, Newton Institute
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