2018-04-04
10:15 at HCP F 43.4

Dynamical low-rank approximation

Christian Lubich

Numerical Analysis Group, Department of Mathematics, Universität Tübingen, Germany

This talk reviews differential equations on manifolds of matrices or tensors of low rank. They serve to approximate, in a low-rank format, large time-dependent matrices and tensors that are either given explicitly via their increments or are unknown solutions of high-dimensional differential equations, such as multi-particle time-dependent Schrödinger equations. Recently developed numerical time integrators are based on splitting the projector onto the tangent space of the low-rank manifold at the current approximation. In contrast to all standard integrators, these projector-splitting methods are robust with respect to the presence of small singular values in the low-rank approximation. This robustness relies on geometric properties of the low-rank manifolds. The talk is based on work done intermittently over the last decade with Othmar Koch, Bart Vandereycken, Ivan Oseledets, Emil Kieri and Hanna Walach.