Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916738532114432 |
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| author | Bachmayr, Markus Eisenmann, Henrik Uschmajew, André |
| author_facet | Bachmayr, Markus Eisenmann, Henrik Uschmajew, André |
| contents | We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16720 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations Bachmayr, Markus Eisenmann, Henrik Uschmajew, André Numerical Analysis 35K15, 35R01 (Primary) 15A69, 65M12 (Secondary) We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors. |
| title | Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations |
| topic | Numerical Analysis 35K15, 35R01 (Primary) 15A69, 65M12 (Secondary) |
| url | https://arxiv.org/abs/2308.16720 |