DOI
10.34229/KCA2522-9664.26.4.9
UDC 519.65
P.S. Malachivskyy
Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics,
National Academy of Sciences of Ukraine, Lviv, Ukraine,
Petro.Malachivskyy@gmail.com
L.S. Melnychok
Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics,
National Academy of Sciences of Ukraine, Lviv, Ukraine,
levkom@gmail.com
O.V. Shevchuk
Lviv Polytechnic National University, Lviv, Ukraine,
oleksii.v.shevchuk@lpnu.ua
CHEBYSHEV APPROXIMATION OF MULTIVARIABLE FUNCTIONS
BY A NONLINEAR FUNCTION FROM A GENERALIZED POLYNOMIAL
WITH A CONDITION
Abstract. A method for constructing Chebyshev approximations of functions of many variables by exponential, logarithmic and power expressions from a generalized polynomial with an interpolation condition is proposed. For this purpose, an intermediate Chebyshev approximation by a generalized polynomial with an interpolation condition of the corresponding functional transformation of the function being approximated is constructed. The approximation by a generalized polynomial is calculated as a limiting mean-power approximation by an iterative scheme using the least squares method with a variable weight function. Test examples are given that confirm the fast convergence of the method.
Keywords: Chebyshev approximation, interpolation condition, multivariable function, nonlinear dependence, modeling, mean-power approximation, least squares method.
full text
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