Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces
Numerical Analysis
2011-12-02 v2 Functional Analysis
Optimization and Control
Abstract
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated Proper Generalized Decompositions for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.
Cite
@article{arxiv.1106.4424,
title = {Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces},
author = {Antonio Falco and Anthony Nouy},
journal= {arXiv preprint arXiv:1106.4424},
year = {2011}
}
Comments
Accepted in Numerische Mathematik