# Probabilistic bounds on best rank-one approximation ratio

arXiv: https://arxiv.org/abs/2201.02191 · HTML: https://mlsanity.com/paper/2201.02191/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [Fast Normalized Cross-Correlation for Template Matching with Rotations](https://mlsanity.com/paper/2311.07561/) (2023)
- [Tensorial template matching for fast cross-correlation with rotations and its application for tomography](https://mlsanity.com/paper/2408.02398/) (2024)

## Abstract (arXiv)

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/√nd-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/√nd-1.