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Volume 61 >>> № 3 MAY — JUNE 2025

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UDC 519.65

P.S. Malachivskyy¹, L.S. Melnychok²

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

Petro.Malachivskyy@gmail.com

² Lviv, Ukraine

levkom@gmail.com

CHEBYSHEV APPROXIMATION BY THE POWER OF A RATIONAL EXPRESSION

Abstract. A method for constructing the Chebyshev approximation of the given function by a rational expression in a fixed power with the smallest relative error is proposed. It consists in constructing an intermediate Chebyshev approximation with a relative error by a rational expression of the values of the root of this power of the approximated function. The rational expression approximation is calculated as a limiting mean-power approximation by an iterative scheme using the least-squares method with two variable weight functions. Test examples are given to confirm the fast convergence of the method for constructing the Chebyshev approximation by the power of a rational expression.

Keywords: Chebyshev approximation by the power expression, Chebyshev approximation by the rational expression, mean-power approximation, least squares method, variable weight function.

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