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SUMMARY:State Estimation in Reduced Modeling - Peter  Binev (University of
  South Carolina)
DTSTART:20180309T090000Z
DTEND:20180309T094500Z
UID:TALK102250@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Albert Cohen		(University Paris 6)\, Wolfgan
 g Dahmen		(University of South Carolina)\, Ronald DeVore		(Texas A&amp\;M 
 University)\, Guergana Petrova		(Texas A&amp\;M University)\, Przemyslaw W
 ojtaszczyk		(University of Warsaw)        <br></span><span><br>We consider
  the problem of optimal recovery of an element u of a Hilbert space H from
  measurements of the form l_j(u)\, j = 1\, ... \, m\, where the l_j are kn
 own linear functionals on H. Motivated by reduced modeling for solving par
 ametric partial diff&#11\;erential equations\, we investigate a setting wh
 ere the additional information about the solution u is in the form of how 
 well u can be approximated by a certain known subspace V_n of H of dimensi
 on n\, or more generally\, in the form of how well u can be approximated b
 y each of a sequence of nested subspaces V_0\, V_1\, ... \, V_n with each 
 V_k of dimension k. The goal is to exploit additional information derived 
 from the whole hierarchy of spaces rather than only from the largest space
  V_n. It is shown that\, in this multispace case\, the set of all u that s
 atisfy the given information can be described as the intersection of a fam
 ily of known ellipsoidal cylinders in H and that a near optimal recovery a
 lgorithm in the multi-space pr oblem is provided by identifying any point 
 in this intersection.</span>
LOCATION:Seminar Room 1\, Newton Institute
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