Eigenvectors of tensors and algorithms for Waring decomposition
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arXiv
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| Format: | Preprint |
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2011
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| _version_ | 1866912649023848448 |
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| author | Oeding, Luke Ottaviani, Giorgio |
| author_facet | Oeding, Luke Ottaviani, Giorgio |
| contents | A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1103_0203 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Eigenvectors of tensors and algorithms for Waring decomposition Oeding, Luke Ottaviani, Giorgio Algebraic Geometry 14Q15, 13P15, 15A18, 15A21 A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem). |
| title | Eigenvectors of tensors and algorithms for Waring decomposition |
| topic | Algebraic Geometry 14Q15, 13P15, 15A18, 15A21 |
| url | https://arxiv.org/abs/1103.0203 |