Iterative thresholding low-rank time integration
Numerical Analysis
2025-07-22 v1 Numerical Analysis
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.
Cite
@article{arxiv.2507.15848,
title = {Iterative thresholding low-rank time integration},
author = {Markus Bachmayr and Matthieu Dolbeault and Polina Sachsenmaier},
journal= {arXiv preprint arXiv:2507.15848},
year = {2025}
}
Comments
35 pages