Approximation in the extended functional tensor train format
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 ev...
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| Published in | Advances in computational mathematics Vol. 50; no. 3 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
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Springer US
01.06.2024
Springer Nature B.V |
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| ISSN | 1019-7168 1572-9044 |
| DOI | 10.1007/s10444-024-10140-9 |
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| 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 et al. (Comput. Methods Appl. Mech. Eng.
347
, 59–84
2019
). |
|---|---|
| AbstractList | 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
$$96\%$$
96
%
compared to the algorithm from Gorodetsky et al. (Comput. Methods Appl. Mech. Eng.
347
, 59–84 2019). 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 et al. (Comput. Methods Appl. Mech. Eng. 347 , 59–84 2019 ). 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 et al. (Comput. Methods Appl. Mech. Eng. 347, 59–84 2019). |
| ArticleNumber | 54 |
| Author | Sun, Bonan Kressner, Daniel Strössner, Christoph |
| Author_xml | – sequence: 1 givenname: Christoph surname: Strössner fullname: Strössner, Christoph email: christoph.stroessner@epfl.ch organization: École Polytechnique Fédérale de Lausanne (EPFL), Institute of Mathematics – sequence: 2 givenname: Bonan surname: Sun fullname: Sun, Bonan organization: École Polytechnique Fédérale de Lausanne (EPFL), Institute of Mathematics – sequence: 3 givenname: Daniel orcidid: 0000-0003-3369-2958 surname: Kressner fullname: Kressner, Daniel organization: École Polytechnique Fédérale de Lausanne (EPFL), Institute of Mathematics |
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| Snippet | This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our... |
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| SubjectTerms | Algorithms Chebyshev approximation Compressing Computational Mathematics and Numerical Analysis Computational Science and Engineering Format Functionals Mathematical analysis Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Tensors Visualization |
| Title | Approximation in the extended functional tensor train format |
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