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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.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 119333, Russia

    N. L. Zamarashkin & A. I. Osinsky

  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    N. L. Zamarashkin

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    N. L. Zamarashkin & A. I. Osinsky

Authors
  1. N. L. Zamarashkin
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  2. A. I. Osinsky
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Corresponding author

Correspondence to A. I. Osinsky.

Additional information

Original Russian Text © N.L. Zamarashkin, A.I. Osinsky, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 5, pp. 489–492.

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Zamarashkin, N.L., Osinsky, A.I. On the Existence of a Nearly Optimal Skeleton Approximation of a Matrix in the Frobenius Norm. Dokl. Math. 97, 164–166 (2018). https://doi.org/10.1134/S1064562418020205

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  • DOI: https://doi.org/10.1134/S1064562418020205

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