Chebyshev approximation by the exponent from a rational expression

A method for constructing Chebyshev approximation with relative error of the exponential from a rational expression is proposed. It implies constructing an intermediate Chebyshev approximation with absolute error by a rational expression of the logarithm of the function being approximated. The approximation by a rational expression is calculated as the boundary mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions. The presented results of solving test examples confirm the fast convergence of the method.