Approximation of smooth surfaces with the double period method

A new method is targeted for approximations of smooth non-periodical $2d$ functions. The idea used for this method is based on special trigonometric mean-square decomposition. Such approach produces smooth approximation and rapidly decreasing decomposition coefficients. The constructed approximations give good precision even on the marginal tabulation area. This allows reasonable extrapolation. The method is illustrated with samples, including practical problems.