Chebyshev approximation of the multivariable functions by some nonlinear expressions

Fìz.-mat. model. ìnf. tehnol. 2021, 33:18-22

Abstract

A method for constructing a Chebyshev approximation of the multivariable functions by exponential, logarithmic and power expressions is proposed. It consists in reducing the problem of the Chebyshev approximation by a nonlinear expression to the construction of an intermediate Chebyshev approximation by a generalized polynomial. The intermediate Chebyshev approximation by a generalized polynomial is calculated for the values of a certain functional transformation of the function we are approximating. The construction of the Chebyshev approximation of the multivariable functions by a polynomial is realized by an iterative scheme based on the method of least squares with a variable weight function.

References

1. Collatz, L.,Krabs, W. (1973). Approximationstheorie: Tschebyscheffsche Approximation mit Anwendungen (Teubner Studienbücher Mathematik). Stuttgart: Teubner Verlag.
2. Popov, B. A., Tesler, G. S. (1980). Approximation of Functions for Engineering Applications [in Russian], Naukova Dumka, Kyiv.
3. Malachivskyy, P. S., Melnychok, L. S., Pizyur, Y. V. (2021). Chebyshev Approximation of Multivariable Functions by The Exponential Expression / Cybernetics and Systems Analysis, 57(3), 429-435.
   DOI https://doi.org/10.1007/s10559-021-00367-5
4. Malachivskyy, P. S., Pizyur, Y. V., Malachivskyi, R. P., Ukhanska, O. M. (2020). Chebyshev approximation of functions of several variables, Cybernetics and Systems Analysis, 56(1), 76–86.
   DOI https://doi.org/10.1007/s10559-020-00227-8