On the Existence of a Nearly Optimal Skeleton Approximation of a Matrix in the Frobenius Norm


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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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