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SUMMARY:"Low-Rank Approximations for High-Dimensional Problems:  Error Est
 imates and Algorithms"
DTSTART:20150310T151500
DTEND:20150310T161500
DTSTAMP:20260407T043500Z
UID:af1415ae009b21d3201a532e4ed8c084365d0efa1b0a388b090dc729
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Markus BACHMAYR (Université Pierre et Marie Curie Paris
  6) \nIn the numerical treatment of high-dimensional operator equations by
  separable approximations\, there have been substantial recent advances co
 ncerning tensor representations that can be regarded as higher-dimensional
  generalizations of the singular value decomposition. The contributions pr
 esented in this talk address the theoretically possible efficiency of such
  approximations for certain problem classes\nas well as their practical nu
 merical computation.\nWe consider two types of high dimensional problems: 
 on the one hand\, multiparametric differential equations\, where the solut
 ion can be regarded as a function depending on spatial and on parametric v
 ariables\; and on the other hand\, high-dimensional elliptic equations (fo
 r instance\, the Poisson equation on a high-dimensional unit cube)\, where
  all variables play the same role.\nThe first part of the talk is concerne
 d with error estimates for low-rank approximation. In particular\, we focu
 s on estimates of Kolmogorov n-widths of solution manifolds of diffusion e
 quations with several parameters. This allows conclusions concerning the p
 erformance that can be achieved by model reduction based on the reduced ba
 sis\nmethod.\nIn the second part of the talk\, we turn to iterative numeri
 cal methods for finding low-rank approximations in hierarchical tensor for
 mats. A crucial problem is here to ensure convergence to the exact solutio
 n while keeping the arising tensor ranks of iterates under control. For an
  iterative scheme based on soft thresholding of tensor representations\, w
 e show convergence with quasi-optimal bounds on the ranks of all\niterates
 .\nThis talk is based on joint projects with Albert Cohen and with Reinhol
 d Schneider.
LOCATION:BI A0 448 (CIB) http://plan.epfl.ch/?lang=fr&room=BI+A0+448+
STATUS:CONFIRMED
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