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Linear approximation of vector functions

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Abstract

In a problem on the approximation of a vector function continuous on an interval by linear functions in the Chebyshev metric, necessary and sufficient conditions on the best approximation function are established.

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References

  1. N. I. Akhiezer, Lectures on Approximation Theory (Nauka, Moscow, 1965) [in Russian].

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  3. A. N. Kolmogorov, “Remark on P.L. Chebyshev’s polynomials least deviating from a given function,” Uspekhi Mat. Nauk 3(1), 216–221 (1948).

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    V. I. Berdyshev

  2. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    V. I. Berdyshev

Authors
  1. V. I. Berdyshev
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Correspondence to V. I. Berdyshev.

Additional information

Original Russian Text © V.I. Berdyshev, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 4.

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Berdyshev, V.I. Linear approximation of vector functions. Proc. Steklov Inst. Math. 288 (Suppl 1), 40–45 (2015). https://doi.org/10.1134/S0081543815020054

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  • DOI: https://doi.org/10.1134/S0081543815020054

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