On implementation of non-polynomial spline approximation

In this paper, different variants of processing of number flows using Lagrange and Hermite non-polynomial splines are studied. The splines are constructed from approximate relations including a generating vector function with components of different character, including non-polynomial. Approximations by first-order Lagrange and third-order Hermite splines are considered. The efficiency of the approximations constructed is demonstrated on the examples of flows of the values of a function and flows of the values of a function and its derivative. The advantages of the splines considered are the simplicity of construction, maximum smoothness, interpolation and approximation properties, and the accuracy on a priori given functions (on the components of the generating vector function).