No. 2025.08
Iterative thresholding low-rank time integration
M. Bachmayr, M. Dolbeault, and P. Sachsenmaier
Subject: Low-rank approximation, evolution equations, quasi-optimal ranks
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.