A linear-time algorithm for Chow decompositions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908535940448256 |
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| author | Blomenhofer, Alexander Taveira Lovitz, Benjamin |
| author_facet | Blomenhofer, Alexander Taveira Lovitz, Benjamin |
| contents | We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm is pencil based, hence it relies on generalized eigenvalue computations. We also develop sub-quadratic time algorithms for higher order Chow decompositions, and Chow decompositions of 3-tensors into products of linear forms which do not lie on the generic orbit. In particular, we obtain a sub-quadratic-time algorithm for decomposing a symmetric 3-tensor into a linear combination of W-tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A linear-time algorithm for Chow decompositions Blomenhofer, Alexander Taveira Lovitz, Benjamin Data Structures and Algorithms Algebraic Geometry Quantum Physics 14Q15, 15A69 We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm is pencil based, hence it relies on generalized eigenvalue computations. We also develop sub-quadratic time algorithms for higher order Chow decompositions, and Chow decompositions of 3-tensors into products of linear forms which do not lie on the generic orbit. In particular, we obtain a sub-quadratic-time algorithm for decomposing a symmetric 3-tensor into a linear combination of W-tensors. |
| title | A linear-time algorithm for Chow decompositions |
| topic | Data Structures and Algorithms Algebraic Geometry Quantum Physics 14Q15, 15A69 |
| url | https://arxiv.org/abs/2509.10450 |