704	RWTH Publication No: 1015396        2025
TITLE	Iterative thresholding low-rank time integration
AUTHORS	Markus Bachmayr, Matthieu Dolbeault, Polina Sachsenmaier
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 Schr¨odinger 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.
KEYWORDS	low-rank approximation, evolution equations, quasi-optimal ranks