Chebyshev approximation of multivariable functions by a nonlinear function of a rational expression

A method for constructing Chebyshev approximations of multivariable functions using an expression that is an exponent, a logarithm, or a fixed real power from a rational expression is proposed. It involves constructing an intermediate Chebyshev approximation by a rational expression of the corresponding functional transformation of the approximated function. The approximation by a rational expression 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 provided that confirm the fast convergence of the method. Keywords: Chebyshev approximation, multivariable function, rational expression, approximation by nonlinear expressions, mean-power approximation, least squares method.