Chebyshev Approximation by Exponential-Power Expression

Abstract

The properties of the Chebyshev approximation by exponential-power expressions with four unknown parameters are investigated. The condition for the existence and uniqueness of such approximation with the smallest relative error is established. A method to determine the parameters of the Chebyshev approximation is proposed and justified. The error of the Chebyshev approximation by the exponential–power expression is estimated.

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Correspondence to P. S. Malachivskyy.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2013, pp. 87–91.

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Malachivskyy, P.S., Pizyur, Y.V., Danchak, N.V. et al. Chebyshev Approximation by Exponential-Power Expression. Cybern Syst Anal 49, 877–881 (2013). https://doi.org/10.1007/s10559-013-9577-1

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Keywords

  • Chebyshev (uniform) approximation
  • points of alternation
  • Remez scheme
  • approximation error