A Greedy Algorithm for Numerical Methods in High Dimension
Langue
en
Communication dans un congrès avec actes
Ce document a été publié dans
International Workshop in Dynamical Systems and Multidisciplinary Applications, 2008, Elche.
Résumé en anglais
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, ...Lire la suite >
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.< Réduire
Mots clés en anglais
Greedy Algorithm
Separated representation
Rank-r approximation
Finite Element Method
Origine
Importé de halUnités de recherche