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Chebyshev Approximation of Multivariable Functions by the Exponential Expression

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Cybernetics and Systems Analysis Aims and scope

Abstract

A method for constructing the Chebyshev approximation of multivariable functions by an exponential expression with a relative error is proposed. It generates an intermediate Chebyshev approximation of the values of the logarithm of a function by a polynomial with the absolute error. An iterative scheme based on the least squares method with a variable weight function is used to construct the Chebyshev approximation of the multivariable functions by a generalized polynomial. The results of solution of the test examples confirm the fast convergence of the method in calculating the parameters of the Chebyshev approximation of the tabular continuous functions of one, two, and three variables.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    P. S. Malachivskyy & L. S. Melnychok

  2. Lviv Polytechnic National University, Lviv, Ukraine

    Ya. V. Pizyur

Authors
  1. P. S. Malachivskyy
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  2. L. S. Melnychok
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  3. Ya. V. Pizyur
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Correspondence to P. S. Malachivskyy.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2021, pp. 106–113.

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Malachivskyy, P.S., Melnychok, L.S. & Pizyur, Y.V. Chebyshev Approximation of Multivariable Functions by the Exponential Expression. Cybern Syst Anal 57, 429–435 (2021). https://doi.org/10.1007/s10559-021-00367-5

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  • DOI: https://doi.org/10.1007/s10559-021-00367-5

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