A. Cohen (LJLL\, UPMC) at Frumam (St Charles): New thoughts on least-square methods

Date(s) : 25/10/2013   iCal
14 h 00 min - 15 h 00 min

New thoughts on least-square methods\n\nBy Albert Cohen\, Laboratoire Jacques Louis Lions\, Paris 6.\n\nLeast squares methods are of common use when one needs to approximate a function based on its noiseless or noisy observation at n scattered points by a simpler function chosen in an m dimensional space with m less than n. Depending on the context\, these points may be randomly drawned according to some distribution\, or deterministically selected by the user.\nIn this talk\, I shall analyze the stability and approximation properties of least squares method. This analysis involves the relative size of m with respect to n as well as the spatial distribution of the samples. Applications will be given for high dimensional sparse polynomial approximation to parametric-stochastic PDE’s and approximation of acoustic fields by plane waves.

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