Chebyshev Approximation by Exponential Expression with Relative Error

Abstract

The properties of the Chebyshev approximation by an exponential expression with the smallest relative error are investigated and the sufficient condition for its existence is established. A method to determine the parameters of such approximation is proposed and justified. The error of the Chebyshev approximation by an exponential expression is estimated. A numerical example confirming the theoretical results is presented.

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Correspondence to P. S. Malachivskyy.

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2015, pp. 145–150.

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Malachivskyy, P.S., Pizyur, Y.V., Danchak, N.V. et al. Chebyshev Approximation by Exponential Expression with Relative Error. Cybern Syst Anal 51, 286–290 (2015). https://doi.org/10.1007/s10559-015-9720-2

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Keywords

  • Chebyshev (uniform) approximation
  • points of alternation
  • relative error
  • kernel of approximation error