On the distance to low-rank matrices in the maximum norm
Numerical Analysis
2025-04-09 v2 Numerical Analysis
Probability
Abstract
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate of the distance for matrices with incoherent column and row spaces. In numerical experiments with several classes of matrices we study how well the theoretical upper bound describes the approximation errors achieved with the method of alternating projections.
Keywords
Cite
@article{arxiv.2312.12905,
title = {On the distance to low-rank matrices in the maximum norm},
author = {Stanislav Budzinskiy},
journal= {arXiv preprint arXiv:2312.12905},
year = {2025}
}
Comments
Accepted version