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New method constructs Chebyshev approximations using rational expressions and nonlinear transformations.
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.
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Malachivskyy et al. (2025) studied this question.
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