On semidefinite programming characterizations of the numerical radius and its dual norm
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911763373490176 |
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| author | Friedland, Shmuel Li, Chi-Kwong |
| author_facet | Friedland, Shmuel Li, Chi-Kwong |
| contents | We state and give self contained proofs of semidefinite programming characterizations of the numerical radius and its dual norm for matrices. We show that the computation of the numerical radius and its dual norm within $\varepsilon$ precision are polynomially time computable in the data and $|\log \varepsilon |$ using either the ellipsoid method or the short step, primal interior point method. We apply our results to give a simple formula for the spectral and nuclear norm of $2\times n\times m$ real tensor in terms of the numerical radius and its dual norm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_07287 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On semidefinite programming characterizations of the numerical radius and its dual norm Friedland, Shmuel Li, Chi-Kwong Numerical Analysis Optimization and Control 15A60, 15A69, 68Q25, 68W25, 81P40, 90C22, 90C51 We state and give self contained proofs of semidefinite programming characterizations of the numerical radius and its dual norm for matrices. We show that the computation of the numerical radius and its dual norm within $\varepsilon$ precision are polynomially time computable in the data and $|\log \varepsilon |$ using either the ellipsoid method or the short step, primal interior point method. We apply our results to give a simple formula for the spectral and nuclear norm of $2\times n\times m$ real tensor in terms of the numerical radius and its dual norm. |
| title | On semidefinite programming characterizations of the numerical radius and its dual norm |
| topic | Numerical Analysis Optimization and Control 15A60, 15A69, 68Q25, 68W25, 81P40, 90C22, 90C51 |
| url | https://arxiv.org/abs/2308.07287 |