Email this article On the existence of a close to optimal cross approximation in the Frobenius norm
- Authors: Osinskii A.I.1,2
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Affiliations:
- Skolkovo Institute of Science and Technology, Moscow, Russia
- Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia
- Issue: Vol 216, No 9 (2025)
- Pages: 69-85
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/309464
- DOI: https://doi.org/10.4213/sm10123
- ID: 309464
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Abstract
We prove that for any matrix, there exists a cross (pseudoskeleton) approximation based on $n$ rows and $n$ columns whose error in the Frobenius norm differs from that of the best possible approximation of the same rank by a factor of at most $1+r/n+o (n^{-1})$, where $r$ is the rank of the cross approximation.
About the authors
Aleksandr Igorevich Osinskii
Skolkovo Institute of Science and Technology, Moscow, Russia; Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia
Author for correspondence.
Email: a.osinskiy@skoltech.ru
Candidate of physico-mathematical sciences
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