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 FUNCTIONS OF SEVERAL VARIABLES
Abstract. The algorithm of uniform approximation for functions of several variables with generalized polynomial is described
as approximation in norm of space Lp
for p → ∞. It is based on sequential construction of power-average approximations using the least squares
method with variable weight function. The convergence of the method provides an original way to consistently refine the values of the
weight function, which takes into account the results of approximation at all previous iterations. Methods of calculating the Chebyshev
approximation with absolute and relative errors are described. The results of test examples confirm the efficiency of using the method
to obtain the Chebyshev approximation of tabular continuous functions of one, two, and three variables.
Keywords: functions of several variables, Chebyshev (uniform) approximation, power-average approximation, least squares method, variable weight function.
FULL TEXT
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