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SUMMARY:Optimal sampling for approximation of functions
DTSTART:20221214T161500
DTEND:20221214T171500
DTSTAMP:20260501T120727Z
UID:e86d54a7f0a2dc4d455aec99bc0ce334e7d260448c71ee9cf0aed5d2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Matthieu Dolbeault (Laboratoire Jacques-Louis Lions\, Sorbonne
  Université)\nIn this talk\, we investigate the problem of approximating 
 a function based on evaluations at some chosen points. A first approach\, 
 using weighted least-squares at i.i.d random points\, provides a near-best
  approximation\, however with a sampling budget larger than the dimension 
 of the approximation space.\nTo reduce the gap between these two quantitie
 s\, we use linear algebra for sums of rank-one matrices\, and in particula
 r the solution to the Kadison-Singer problem. This leads to sharp estimat
 es\, both in a randomized setting for L^2 functions\, and in a determinist
 ic setting for reproducing kernel Hilbert spaces.
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CONFIRMED
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