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SUMMARY:High dimensional sparse approximation of elliptic PDEs with lognor
 mal coefficients - Albert Cohen (Laboratoire Jacques-Louis Lions\, Univers
 ité Pierre et Marie Curie)
DTSTART:20160211T150000Z
DTEND:20160211T160000Z
UID:TALK62826@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Various mathematical problems are challenged by the fact they 
 involve functions of a very large number\nof variables. Such problems aris
 e naturally in learning theory\, partial differential equations or numeric
 al models\ndepending on parametric or stochastic variables. They typically
  result in numerical difficulties due to\nthe so-called ''curse of dimensi
 onality''. We shall discuss the particular example of elliptic partial dif
 ferential \nequations with diffusion coefficients of lognormal form\, that
  is\, of the form exp(b) where b is a gaussian random field. \nThe numeric
 al strategy consists in searching for a sparse polynomial approximation by
  best n-term truncation of\ntensorized Hermite expansions in stochastic va
 riables which represent the gaussian fields. One interesting conclusion \n
 from our analysis  is that in certain relevant cases\, the often used Karh
 unen–Loeve representation might not be \nthe best choice  in terms of th
 e resulting sparsity and approximability of Hermite expansion.
LOCATION:MR 14\, CMS
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