Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910852068671488 |
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| author | Fang, Lishan Huang, Hua-Lin Li, Yuechen |
| author_facet | Fang, Lishan Huang, Hua-Lin Li, Yuechen |
| contents | We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials Fang, Lishan Huang, Hua-Lin Li, Yuechen Rings and Algebras Number Theory 15A20, 15A69 We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity. |
| title | Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials |
| topic | Rings and Algebras Number Theory 15A20, 15A69 |
| url | https://arxiv.org/abs/2310.14042 |