On the optimal approximation of geophysical fields

In this paper, optimal methods of approximation of some geophysical fields involving gravitational and heat fields are considered. A review of results on this problem is presented. We have developed the algorithm of approximation of multidimensional heat fields which are described by heat equation with constant coefficients. In order to do that, we introduce classes of functions that include solutions of heat equations, and continuous splines uniformly approximating the functions from these classes in the whole domain of definition. We give the upper bounds for the Kolmogorov diameters of the introduced classes of functions.For a wider class of the introduced classes of functions, the Kolmogorov diameters is estimated from below.