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  4. Chebyshev approximation of multivariable functions with the interpolation

Chebyshev approximation of multivariable functions with the interpolation

MMC.
2022;
Volume 9, Number 3
: pp. 757–766
https://doi.org/10.23939/mmc2022.03.757
Received: May 22, 2022
Revised: August 27, 2022
Accepted: August 31, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 757–766 (2022)

Authors:
  1. P. Malachivskyy
  2. L. Melnychok
  3. Ya. Pizyur
1
Pidstryhach Institute for Applide Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
2
Pidstryhach Institute for Applide Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
3
Lviv Polytechnic National University

A method of constructing a Chebyshev approximation of multivariable functions by a generalized polynomial with the exact reproduction of its values at a given points is proposed.  It is based on the sequential construction of mean-power approximations, taking into account the interpolation condition.  The mean-power approximation is calculated using an iterative scheme based on the method of least squares with the variable weight function.  An algorithm for calculating the Chebyshev approximation parameters with the interpolation condition for absolute and relative error is described.  The presented results of solving test examples confirm the rapid convergence of the method when calculating the parameters of the Chebyshev approximation of tabular continuous functions of one, two and three variables with the reproduction of the values of the function at given points.

Chebyshev approximation with the interpolation condition
multivariable functions
mean-power approximation
least squares method
variable weight function
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