Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.02191 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909126156615680 |
|---|---|
| author | Kozhasov, Khazhgali Tonelli-Cueto, Josué |
| author_facet | Kozhasov, Khazhgali Tonelli-Cueto, Josué |
| contents | We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric tensors our upper bound unveils that the ratio of norms has the same order of magnitude as the trivial lower bound $1/\sqrt{n^{d-1}}$, when the order of a tensor $d$ is fixed and the dimension of the underlying vector space $n$ tends to infinity. However, when $n$ is fixed and $d$ tends to infinity, our lower bound is better than $1/\sqrt{n^{d-1}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_02191 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Probabilistic bounds on best rank-one approximation ratio Kozhasov, Khazhgali Tonelli-Cueto, Josué Functional Analysis Optimization and Control Probability 15A69, 26C05, 41A50 We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric tensors our upper bound unveils that the ratio of norms has the same order of magnitude as the trivial lower bound $1/\sqrt{n^{d-1}}$, when the order of a tensor $d$ is fixed and the dimension of the underlying vector space $n$ tends to infinity. However, when $n$ is fixed and $d$ tends to infinity, our lower bound is better than $1/\sqrt{n^{d-1}}$. |
| title | Probabilistic bounds on best rank-one approximation ratio |
| topic | Functional Analysis Optimization and Control Probability 15A69, 26C05, 41A50 |
| url | https://arxiv.org/abs/2201.02191 |