Chebyshev Approximation of a Multivariable Function with Reproducing the Values of the Function and Its Partial Derivatives

The method for constructing the Chebyshev approximation of a discrete multivariable function with reproducing the values of the function and its partial derivatives at given points is proposed. The method is based on constructing a boundary mean-power approximation with appropriate interpolation conditions. The authors use an iterative scheme based on the least squares method with a variable weight function for constructing the mean-power approximation. The results of approximating the one-variable function confirm the fulfillment of the characteristic feature of the Chebyshev approximation with the reproduction of the function and its derivative values at given points. The test examples instantiate the fast convergence of the proposed method.