CHEBYSHEV APPROXIMATION OF THE MULTIVARIABLE FUNCTIONS BY POWER EXPRESSION

Abstract

A method of constructing the Chebyshev approximation with the smallest relative error of multivariable functions by a power expression is proposed. It consists in constructing an intermediate Chebyshev approximation of the function, which is the root of the corresponding power of the given function by a polynomial. The parameters of the polynomial approximation are calculated as the limiting mean-power approximation according to the iterative scheme using the least squares method with a variable weight function. Test examples are given that confirm the fast convergence of the method of constructing the Chebyshev approximation using the power expression of functions of one, two, and three variables. Keywords: Chebyshev approximation of the multivariable functions, power expression, mean-power approximation, least squares method, variable weight function.