Chebyshev approximation of multivariable functions by the rational expression with the condition / Malachivskyy, / Melnychok, / Pizyur. (2023)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2023, 59 (1))

Malachivskyy P.S., Melnychok L.S., Pizyur Y.V.
Chebyshev approximation of multivariable functions by the rational expression with the condition

The method for constructing the Chebyshev approximation of multivariable functions by a logarithmic expression with an absolute error is proposed. It implies constructing an intermediate Chebyshev approximation of the values of the exponent of an approximated function by a polynomial with the relative error. The construction of the Chebyshev approximation by a polynomial is based on calculating the boundary mean-power approximation by an iterative scheme based on the least squares method with properly formed values of variable weight function. The presented results of test examples’ solving confirm the fast convergence of the method in calculating the parameters of the Chebyshev approximation of the functions of one, two, and three variables by the logarithmic expression. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Chebyshev approximation of the multivariable functions, least squares method, logarithmic expression, mean-power approximation, variable weight function, Iterative methods, Least squares approximations, Multivariable systems, Absolute error, Chebyshev approximation of the multivariable function, Least-squares- methods, Logarithmic expression, Mean power, Mean-power approximation, Variable weight, Variable weight function, Weight functions, Polynomial approximation


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Cite:
Malachivskyy P.S., Melnychok L.S., Pizyur Y.V. (2023). Chebyshev approximation of multivariable functions by the rational expression with the condition. Cybernetics and Systems Analysis, 59 (1), 169–179. doi: https://doi.org/10.1007/s10559-023-00565-3 http://jnas.nbuv.gov.ua/article/UJRN-0001380513 [In Ukrainian].


 

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