Mathematics > Numerical Analysis
arXiv:2211.11338 (math)
[Submitted on 21 Nov 2022 (v1), last revised 25 Feb 2024 (this version, v3)]
Title:Approximation in the extended functional tensor train format
View a PDF of the paper titled Approximation in the extended functional tensor train format, by Christoph Str\"ossner and Bonan Sun and Daniel Kressner
View PDFHTML (experimental)Abstract:This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. Compared to existing methods based on the functional tensor train format, the adaptivity of our approach often results in reducing the required storage, sometimes considerably, while achieving the same accuracy. In particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96% compared to the algorithm from [Gorodetsky, Karaman and Marzouk, Comput. Methods Appl. Mech. Eng., 347 (2019)].
| Subjects: | Numerical Analysis (math.NA) |
| Cite as: | arXiv:2211.11338 [math.NA] |
| (orarXiv:2211.11338v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2211.11338 arXiv-issued DOI via DataCite | |
| Related DOI: | https://doi.org/10.1007/s10444-024-10140-9 DOI(s) linking to related resources |
Submission history
From: Christoph Strössner [view email][v1] Mon, 21 Nov 2022 10:38:48 UTC (436 KB)
[v2] Thu, 14 Sep 2023 17:54:19 UTC (294 KB)
[v3] Sun, 25 Feb 2024 15:09:08 UTC (452 KB)
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View a PDF of the paper titled Approximation in the extended functional tensor train format, by Christoph Str\"ossner and Bonan Sun and Daniel Kressner
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