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Tr. Mat. Inst. Steklova, 2018, Volume 303, Pages 155–168 (Mi tm3950)  

Kolmogorov width and approximate rank

B. S. Kashinab, Yu. V. Malykhinab, K. S. Ryutinb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Laboratory "High-Dimensional Approximation and Applications", Lomonosov Moscow State University, Moscow, 119991 Russia

Abstract: Closely related notions of the Kolmogorov width and the approximate rank of a matrix are considered. New estimates are established in approximation problems related to the width of the set of characteristic functions of intervals; the multidimensional case (characteristic functions of parallelepipeds) is also considered.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
This work was supported by a grant of the Government of the Russian Federation (contract no. 14.W03.31.0031).


DOI: https://doi.org/10.1134/S037196851804012X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 303, 140–153

Bibliographic databases:

UDC: 517.518.8
Received: May 30, 2018

Citation: B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Tr. Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 155–168; Proc. Steklov Inst. Math., 303 (2018), 140–153

Citation in format AMSBIB
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\paper Kolmogorov width and approximate rank
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 155--168
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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