Email this article On the Existence of a Nearly Optimal Skeleton Approximation of a Matrix in the Frobenius Norm
- Authors: Zamarashkin N.L.1,2,3, Osinsky A.I.1,3
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Affiliations:
- Institute of Numerical Mathematics
- Faculty of Computational Mathematics and Cybernetics
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 97, No 2 (2018)
- Pages: 164-166
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225483
- DOI: https://doi.org/10.1134/S1064562418020205
- ID: 225483
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Abstract
For an arbitrary matrix, we prove the existence of a skeleton approximation of rank r whose accuracy estimate is only r + 1 times worse than the estimate of the optimal approximation of rank r in the Frobenius norm.
About the authors
N. L. Zamarashkin
Institute of Numerical Mathematics; Faculty of Computational Mathematics and Cybernetics; Moscow Institute of Physics and Technology (State University)
Email: sasha_o@list.ru
Russian Federation, Moscow, 119333; Moscow, 119991; Dolgoprudnyi, Moscow oblast, 141700
A. I. Osinsky
Institute of Numerical Mathematics; Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: sasha_o@list.ru
Russian Federation, Moscow, 119333; Dolgoprudnyi, Moscow oblast, 141700
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