The Generalized Matrix Norm Problem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866912664362418176 |
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| author | Kulmburg, Adrian |
| author_facet | Kulmburg, Adrian |
| contents | We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can be approximated in other cases. Along the way, we investigate the concept of push-forward and pull-back of seminorms, which leads us to uncover novel duality principles that come into play when optimizing over the unit ball of norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00605 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Generalized Matrix Norm Problem Kulmburg, Adrian Numerical Analysis 15A60 (Primary), 65F35, 68Q25 We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can be approximated in other cases. Along the way, we investigate the concept of push-forward and pull-back of seminorms, which leads us to uncover novel duality principles that come into play when optimizing over the unit ball of norms. |
| title | The Generalized Matrix Norm Problem |
| topic | Numerical Analysis 15A60 (Primary), 65F35, 68Q25 |
| url | https://arxiv.org/abs/2310.00605 |