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arXiv · 2507.15848

Iterative thresholding low-rank time integration

Markus Bachmayr·Matthieu Dolbeault·Polina Sachsenmaier
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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.

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Markus Bachmayr, Matthieu Dolbeault, Polina Sachsenmaier. 2025-07-21. Iterative thresholding low-rank time integration. https://arxiv.org/abs/2507.15848

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