Shepard approximation method and its applications

The Shepard approximation method - one of the little-known ways to build static models based on " irregular data ", in which the set of nodes of learning samples is random. Shepard function is the ratio of two rational functions ("fractional rational function"), for the construction of which, in contrast to other methods of approximation, does not require solution of optimization problems. The report examines the properties of Shepard function and the proposed modifications and its application to solving problems of data mining, a non-convex optimization and optimal control.