About one method of construction of interpolation trigonometric splines

V.Denysiuk

The method of constructing spline classes in the form of trigonometric
Fourier series whose coefficients have a certain decreasing order are
considered. in turn, this decrement determines the number of continuous
derivatives of sum of this series. By grouping members of this series according
with the effect of overlaying and introducing a multiplier that provides the
interpolation properties of the sum of these series on even grids, we obtain
classes of trigonometric interpolation splines. Depending on the types of
convergence factors with a certain decreasing order, different classes of such
splines are obtained. The classes of trigonometric splines include classes of
periodic polynomial splines of even and odd power; At the same time, there
exist trigonometric splines that do not have polynomial analogues. An example
of the construction of trigonometric splines is given.