UDC 519.65
1 Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine
 Petro.Malachivskyy@gmail.com
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2 Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine
levkom@gmail.com
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CHEBYSHEV APPROXIMATION OF MULTIVARIABLE FUNCTIONS
BY A LOGARITHMIC EXPRESSION
Abstract. A method for constructing a Chebyshev approximation of the multivariable functions by a logarithmic expression with absolute error is proposed. It implies constructing an intermediate Chebyshev approximation by a polynomial with the relative error of the exponential value of the function being approximated. Construction of the Chebyshev approximation by a polynomial is based on calculating the limit mean-power approximation by the least squares method in accordance with the prevailing values of the variable weight function. The presented results of solving test examples confirm the rapid convergence of the method when calculating the parameters of the Chebyshev approximation by the logarithmic expression of the functions of one, two, and three variables.
Keywords: Chebyshev approximation of the multivariable functions, logarithmic expression, mean-power approximation, least squares method, variable weight function.
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