A Greedy Algorithm for Numerical Methods in High Dimension
Language
en
Communication dans un congrès avec actes
This item was published in
International Workshop in Dynamical Systems and Multidisciplinary Applications, 2008, Elche.
English Abstract
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, ...Read more >
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.Read less <
English Keywords
Greedy Algorithm
Separated representation
Rank-r approximation
Finite Element Method
Origin
Hal imported