624
|
RWTH Publication No: 974379 2023   |
TITLE |
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations |
AUTHORS |
Markus Bachmayr, Henrik Eisenmann, André Uschmajew |
ABSTRACT |
We consider dynamical low-rank approximations to parabolic problems on
higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and
their stability with respect to perturbations to the problem data, we show convergence of
spatial discretizations. Our framework accommodates various standard low-rank tensor
formats for multivariate functions, including tensor train and hierarchical tensors. |
KEYWORDS |
low-rank approximation, tensor train, hierarchical tensors |