Interval Estimation of Polynomial Splines of the Fifth Order

In many cases, approximation by local interpolating splines is preferable to approximation by interpolating polynomials or interpolating by other types of splines. In the case of integro-differential splines we use the values of integrals over net intervals. The main features of these splines are the following: the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed as the sum of products of the basic splines and the values of function in nodes and/or the values of its derivatives and/or the values of integrals of this function over subintervals. Basic splines are determined by using a solving system of equations which are provided by the set of functions. In this paper we present the estimation of approximation and the algorithm for constructing an interval extension of approximation when values of function in nodes, values of its first derivative in nodes, and values of its integrals over net intervals are given. The algorithm of approximation is based on the method of approximating functions using integro-differential splines. For constructing this interval extension, we use techniques from interval analysis. Numerical examples are given.