Chebyshev Approximation of the Functions of Many Variables with the Condition

A method of constructing a Chebyshev approximation of the function of many variables with the exact reproduction of its value at a given point is proposed. It is based on the sequential construction of mean-power approximations, taking into account the imposed condition. The mean-power approximation is calculated using an iterative scheme based on the method of least squares with the variable weight function. An algorithm for calculating the Chebyshev approximation parameters with a condition for absolute error is described.