On the distance to low-rank matrices in the maximum norm

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...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Author: Budzinskiy, Stanislav
Format: Article
Language:English
Subjects:
Matrices (mathematics)
Upper bounds
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2312.12905