Interval estimation of trigonometrical splines

I.G. Burova, E.G. Ivanova, V.A. Kostin, A. Bulucea, V. Mladenov, N. Mastorakis
2019 MATEC Web of Conferences  
Quite often, it is necessary to quickly determine variation range of the function. If the function values are known at some points, then it is easy to construct the local spline approximation of this function and use the interval analysis rules. As a result, we get the area within which the approximation of this function changes. It is necessary to take into account the approximation error when studying the obtained area of change of function approximation. Thus, we get the range of changing
more » ... ange of changing the function with the approximation error. This paper discusses the features of using polynomial and trigonometrical splines of the third order approximation to determine the upper and lower boundaries of the area (domain) in which the values of the approximation are contained. Theorems of approximation by these local trigonometric and polynomial splines are formulated. The values of the constants in the estimates of the errors of approximation by the trigonometrical and polynomial splines are given. It is shown that these constants cannot be reduced. An algorithm for constructing the variation domain of the approximation of the function is described. The results of the numerical experiments are given.
doi:10.1051/matecconf/201929203001 fatcat:3i7njesvkjbxfj3ennaoc2nnvu