Adaptive low-rank approximations for stochastic and parametric equations: a subspace point of view | Vidéo | Carmin.tv

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Adaptive low-rank approximations for stochastic and parametric equations: a subspace point of view

By Anthony Nouy

Appears in collection : MoMaS Conference / Colloque MoMaS

Tensor methods have emerged as an indispensable tool for the numerical solution of high-dimensional problems in computational science, and in particular problems arising in stochastic and parametric analyses. In many practical situations, the approximation of functions of multiple parameters (or random variables) is made computationally tractable by using low-rank tensor formats. Here, we present some results on rank-structured approximations and we discuss the connection between best approximation problems in tree-based low-rank formats and the problem of finding optimal low-dimensional subspaces for the projection of a tensor. Then, we present constructive algorithms that adopt a subspace point of view for the computation of sub-optimal low-rank approximations with respect to a given norm. These algorithms are based on the construction of sequences of suboptimal but nested subspaces.

Keywords: high dimensional problems - tensor numerical methods - projection-based model order reduction - low-rank tensor formats - greedy algorithms - proper generalized decomposition - uncertainty quantification - parametric equations

Information about the video

Date of recording 19/11/2014
Date of publication 27/11/2014
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18630403
Cite this video Nouy, Anthony (19/11/2014). Adaptive low-rank approximations for stochastic and parametric equations: a subspace point of view. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18630403
URL https://dx.doi.org/10.24350/CIRM.V.18630403

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Bibliography

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