Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
- 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.
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| Author: | Markus Bachmayr, Henrik Eisenmann, André UschmajewGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1218617 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/121861 |
| ISSN: | 0029-599XOPAC |
| ISSN: | 0945-3245OPAC |
| Parent Title (German): | Numerische Mathematik |
| Publisher: | Springer Science and Business Media LLC |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2025 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/05/09 |
| Volume: | 157 |
| First Page: | 781 |
| Last Page: | 822 |
| DOI: | https://doi.org/10.1007/s00211-025-01465-8 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Mathematical Data Science | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
