C&SA | Contents

Volume 61 >>> № 1 JANUARY — FEBRUARY 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 LOGARITHM OF A RATIONAL EXPRESSION

Abstract. A method for constructing the Chebyshev approximation with absolute error by the logarithm of a rational expression is proposed. It is to construct an intermediate Chebyshev approximation by a rational expression with a relative error of the exponent of the approximated function. The approximation by the rational expression is calculated as the boundary of mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The presented results of solving test examples confirm the fast convergence of the method.

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

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