A Greedy Algorithm for Numerical Methods in High Dimension
| hal.structure.identifier | Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA] | |
| dc.contributor.author | AMMAR, Amine | |
| hal.structure.identifier | Institut de Recherche en Génie Civil et Mécanique [GeM] | |
| dc.contributor.author | CHINESTA, Francisco | |
| hal.structure.identifier | Departamento de Ciencias, Físicas, Matemáticas y de la Computación | |
| dc.contributor.author | FALCÓ, Antonio | |
| dc.date.accessioned | 2021-05-14T09:49:36Z | |
| dc.date.available | 2021-05-14T09:49:36Z | |
| dc.date.conference | 2008 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/77228 | |
| dc.description.abstractEn | In this work we study the problem of compute the best rank-r approximation to the solution of a class of linear systems. It arises in the discretized equations appearing in various physical domains, such as kinetic theory, statistical mechanics, quantum mechanics,and in nano-science and nanotechnology among others. In particular, we use the fact that tensors of order 3 or higher have best rank-1 approximation. Then we propose an iterative method such that at step-n we are to be able to compute an approximate solution of rank-n satisfying an optimal condition. Finally, we describe its relationship with the Finite Element Method for High-Dimensional Partial Differential Equations based on the tensorial product of one-dimensional bases. We illustrate this situation taking as a model problem the multidimensional Poisson equation with homogeneous Dirichlet boundary condition. | |
| dc.language.iso | en | |
| dc.subject.en | Greedy Algorithm | |
| dc.subject.en | Separated representation | |
| dc.subject.en | Rank-r approximation | |
| dc.subject.en | Finite Element Method | |
| dc.title.en | A Greedy Algorithm for Numerical Methods in High Dimension | |
| dc.type | Communication dans un congrès avec actes | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Matériaux | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| bordeaux.country | ES | |
| bordeaux.title.proceeding | International Workshop in Dynamical Systems and Multidisciplinary Applications | |
| bordeaux.conference.city | Elche | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01007749 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01007749v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMMAR,%20Amine&CHINESTA,%20Francisco&FALC%C3%93,%20Antonio&rft.genre=proceeding |
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