On the Best Approximation Algorithm by Low-Rank Matrices in Chebyshev’s Norm

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 resul...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2022, Vol.62 (5), p.701-718
Main Authors: Zamarashkin, N. L., Morozov, S. V., Tyrtyshnikov, E. E.
Format: Article
Language:English
Subjects:
Algorithms
Chebyshev approximation
Computational Mathematics and Numerical Analysis
General Numerical Methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542522050141