CP decomposition and low-rank approximation of antisymmetric tensors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910687283904512 |
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| author | Begovic, Erna Perisa, Lana |
| author_facet | Begovic, Erna Perisa, Lana |
| contents | For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for finding such approximation. Moreover, we show that this approximation problem is equivalent to the problem of finding the best multilinear low-rank antisymmetric approximation and, consequently, equivalent to the problem of finding the best unstructured rank-$1$ approximation. The case of partial antisymmetry is also discussed. The algorithms are implemented in Julia programming language and their numerical performance is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13389 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | CP decomposition and low-rank approximation of antisymmetric tensors Begovic, Erna Perisa, Lana Numerical Analysis 15A69 For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for finding such approximation. Moreover, we show that this approximation problem is equivalent to the problem of finding the best multilinear low-rank antisymmetric approximation and, consequently, equivalent to the problem of finding the best unstructured rank-$1$ approximation. The case of partial antisymmetry is also discussed. The algorithms are implemented in Julia programming language and their numerical performance is discussed. |
| title | CP decomposition and low-rank approximation of antisymmetric tensors |
| topic | Numerical Analysis 15A69 |
| url | https://arxiv.org/abs/2212.13389 |