Chebyshev Approximation of Multivariable Functions by a Constrained Rational Expression

The authors propose a method for constructing the Chebyshev approximation of multivariable functions by the rational expression with the interpolation condition. The idea of the method is based on constructing the limiting power mean approximation by a rational expression with an interpolation condition in the norm of space L p as p → ∞. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions is used. One weight function ensures the construction of a power mean approximation with the interpolation condition, and the second one specifies the parameters of the rational expression according to its linearization scheme. The convergence of the method is provided by the original method of sequential specification of the values of weight functions, which takes into account the approximation results at previous iterations. The results of test examples confirm the fast convergence of the proposed method of constructing the Chebyshev approximation by a rational expression with a condition.