Trace maximization algorithm for the approximate tensor diagonalization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911801692651520 |
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| author | Begovic, Erna Boksic, Ana |
| author_facet | Begovic, Erna Boksic, Ana |
| contents | In this paper we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order $d\geq3$ via tensor trace maximization. For a general tensor this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand, for symmetric tensors we discuss a structure-preserving variant of this algorithm where in each iteration the same rotation is applied in all modes. We show that both versions of the algorithm converge to the stationary points of the corresponding objective functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_01466 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Trace maximization algorithm for the approximate tensor diagonalization Begovic, Erna Boksic, Ana Numerical Analysis 15A69, 65F25, 65F99 In this paper we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order $d\geq3$ via tensor trace maximization. For a general tensor this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand, for symmetric tensors we discuss a structure-preserving variant of this algorithm where in each iteration the same rotation is applied in all modes. We show that both versions of the algorithm converge to the stationary points of the corresponding objective functions. |
| title | Trace maximization algorithm for the approximate tensor diagonalization |
| topic | Numerical Analysis 15A69, 65F25, 65F99 |
| url | https://arxiv.org/abs/2111.01466 |