Iterative thresholding low-rank time integration

RWTH Publications (RWTH Aachen)

Abstract

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation ranks. Our approach relies on an iterative scheme combined with soft thresholding of the iterates. A model case of a time-dependent Schrödinger equation with low-rank matrix approximation is analyzed in detail, and the required modifications for second-order parabolic problems are described. Numerical tests illustrate the results for both cases.

Authors 3

1. Markus Bachmayr Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

   IGPM - Institut für Geometrie und Praktische Mathematik [RWTH Aachen] (Templergraben 55, D-52056 Aachen, Germany - Germany)

2. Matthieu Dolbeault Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

   IGPM - Institut für Geometrie und Praktische Mathematik [RWTH Aachen] (Templergraben 55, D-52056 Aachen, Germany - Germany)

3. Polina Sachsenmaier Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

   IGPM - Institut für Geometrie und Praktische Mathematik [RWTH Aachen] (Templergraben 55, D-52056 Aachen, Germany - Germany)