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Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation

  • Systems Analysis
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Cybernetics and Systems Analysis Aims and scope

Sufficient existence conditions are established for the uniform Chebyshev (minimax) approximation of a function by the sum of a polynomial and an expression with a nonlinear parameter with the minimum absolute error and interpolation at the interval endpoints. An algorithm for determining the parameters of such an approximation using the Remez algorithm is proposed. The application of the iterative method to calculating the nonlinear parameter is substantiated.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. V. Skopetskii

  2. Center for Mathematical Modeling, Ya. S. Pidstruhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, L’viv, Ukraine

    P. S. Malachivskii

Authors
  1. V. V. Skopetskii
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  2. P. S. Malachivskii
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Correspondence to V. V. Skopetskii.

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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 64–75, January–February 2009.

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Skopetskii, V.V., Malachivskii, P.S. Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation. Cybern Syst Anal 45, 58–68 (2009). https://doi.org/10.1007/s10559-009-9078-4

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  • DOI: https://doi.org/10.1007/s10559-009-9078-4

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