CHEBYSHEV APPROXIMATION BY THE POWER OF A RATIONAL EXPRESSION

A method for constructing the Chebyshev approximation of the given function by a rational expression in a fixed power with the smallest relative error is proposed. It consists in constructing an intermediate Chebyshev approximation with a relative error by a rational expression of the values of the root of this power of the approximated function. The rational expression approximation is calculated as a limiting mean-power approximation by an iterative scheme using the least-squares method with two variable weight functions. Test examples are given to confirm the fast convergence of the method for constructing the Chebyshev approximation by the power of a rational expression. Keywords: Chebyshev approximation by the power expression, Chebyshev approximation by the rational expression, mean-power approximation, least squares method, variable weight function.