Applied Physics and Mathematics Annotation << Back ABOUT NEW “IDEOLOGY” OF INTERPOLATION WITH STRUCTURE-FORMING FUNCTIONS V.I. RAKOV The important role of nonlinear functions is noted at the description of dynamics of management processes by means of the differential equations. Reliability of formation of operating influences depends on the accuracy of reproduction of nonlinear functions. Features of approximations in the mean and the minimax approximations are specified. They can cardinally change nature of derivative described functions. It can influence reliability of calculated operating influences. The preference of use of interpolation approach is noted at creation of analytical descriptions. Possibilities of use of the main interpolation functions and those problem questions which accompany their application are estimated. Relevance of development of new methods of interpolation and creation of the appropriate program tools for their realization is shown. The new interpolation formula and its interpretation, constructed on the basis of use of structure-forming functions is offered. Structure-forming functions allow to pass quickly to various interpolation formulas, knots and provide possibilities of regulation of an error of the description. On an example efficiency of use on small number of knots of approximation is shown. Keywords: control, model, interpolation, approximation, digital approximation, mathematical approximation, minimax approximation, rational approximation, successive approximation, weighted approximation Contacts: E-mail: rakov2010vi@mail.ru Pp. 24-47.