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SUMMARY:Hierarchical Low Rank Tensors - Lars Grasedyck (RWTH Aachen Univer
 sity)
DTSTART:20180307T090000Z
DTEND:20180307T094500Z
UID:TALK102217@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Sebastian Kr&auml\;mer\, Christian L&ouml\;bbert\,
  Dieter Moser (RWTH Aachen)  We introduce the concept of hierarchical low 
 rank decompositions and approximations by use of the hierarchical Tucker f
 ormat. In order to relate it to several other existing low rank formats we
  highlight differences\, similarities as well as bottlenecks of these. One
  particularly difficult question is whether or not a tensor or multivariat
 e function allows a priori a low rank representation or approximation. Thi
 s question can be related to simple matrix decompositions or approximation
 s\, but still the question is not easy to answer\, cf. the talks of Wolfga
 ng Dahmen\, Sergey Dolgov\, Martin Stoll and Anthony Nouy. We provide nume
 rical evidence for a model problem that the approximation can be efficient
  in terms of a small rank. In order to find such a decomposition or approx
 imation we consider black box (cross) type non-intrusive sampling approach
 es. A special emphasis will be on postprocessing of the tensors\, e.g. fin
 ding extremal points efficiently. This is of special interest in the conte
 xt of model reduction and reliability analysis.
LOCATION:Seminar Room 1\, Newton Institute
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