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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CHEBYSHEV APPROXIMATION OF MULTIVARIABLE FUNCTIONS WITH
REPRODUCTION OF THE VALUES OF THE FUNCTION AND ITS PARTIAL DERIVATIVES
Abstract. A method for constructing the Chebyshev approximation of a discrete multivariable function with reproduction of function’s values and partial derivatives at given points is proposed. The idea of the method is based on the construction of the boundary mean-power approximation with the appropriate interpolation conditions. An iterative scheme based on the least squares method with a variable weight function is used to construct the mean-power approximation. The results of the approximation of the function of one variable confirm the fulfillment of the characteristic property of the Chebyshev approximation with the reproduction of the values of the function and the values of its derivatives at the given points. The test examples confirm the fast convergence of the proposed method.
Keywords: Chebyshev approximation, Chebyshev approximation with the condition, multivariable functions, mean-power approximation, least squares method, variable weight function, partial derivatives.
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