Iterative thresholding low-rank time integration
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915403017486336 |
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| author | Bachmayr, Markus Dolbeault, Matthieu Sachsenmaier, Polina |
| author_facet | Bachmayr, Markus Dolbeault, Matthieu Sachsenmaier, Polina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative thresholding low-rank time integration Bachmayr, Markus Dolbeault, Matthieu Sachsenmaier, Polina Numerical Analysis Primary 65F55, 65M12, Secondary 65Y20, 65L70 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. |
| title | Iterative thresholding low-rank time integration |
| topic | Numerical Analysis Primary 65F55, 65M12, Secondary 65Y20, 65L70 |
| url | https://arxiv.org/abs/2507.15848 |