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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 5, Pages 723–741
DOI: https://doi.org/10.31857/S0044466922050143 (Mi zvmmf11392) 		 
This article is cited in 4 scientific papers (total in 4 papers)

General numerical methods

On the best approximation algorithm by low-rank matrices in Chebyshev's norm

N. L. Zamarashkin, S. V. Morozov, E. E. Tyrtyshnikov

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
Citations (4)
DOI: https://doi.org/10.31857/S0044466922050143
Abstract: The problem of approximation by low-rank matrices is found everywhere in computational mathematics. Traditionally, this problem is solved in the spectral or Frobenius norm, where the approximation efficiency is associated with the rate of decrease of the matrix singular values. However, recent results show that this requirement is not necessary in other norms. In this paper, a method for solving the problem of approximating by low-rank matrices in Chebyshev’s norm is proposed. It makes it possible to construct effective approximations of matrices for which singular values do not decrease in an acceptable amount time.
Key words: approximation by low-rank matrices, Remez algorithm, Chebyshev's approximation.
Funding agency Grant number
Russian Science Foundation 21-71-10072
This work was supported by the Russian Science Foundation, project no. 21-71-10072.
Received: 18.11.2021
Revised: 18.11.2021
Accepted: 16.12.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 5, Pages 701–718
DOI: https://doi.org/10.1134/S0965542522050141
Bibliographic databases:
Document Type: Article
UDC: 517.983.3+512.643.8
Language: Russian
Citation: N. L. Zamarashkin, S. V. Morozov, E. E. Tyrtyshnikov, “On the best approximation algorithm by low-rank matrices in Chebyshev's norm”, Zh. Vychisl. Mat. Mat. Fiz., 62:5 (2022), 723–741; Comput. Math. Math. Phys., 62:5 (2022), 701–718
Citation in format AMSBIB
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\by N.~L.~Zamarashkin, S.~V.~Morozov, E.~E.~Tyrtyshnikov
\paper On the best approximation algorithm by low-rank matrices in Chebyshev's norm
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 5
\pages 723--741
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\crossref{https://doi.org/10.31857/S0044466922050143}
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\elib{https://elibrary.ru/item.asp?id=48506047}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 5
\pages 701--718
\crossref{https://doi.org/10.1134/S0965542522050141}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85132177224}
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  • https://www.mathnet.ru/eng/zvmmf/v62/i5/p723
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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