About some aspects of function interpolation by trigonometric splines

TL;DR

This paper explores a method for interpolating differentiated functions using trigonometric splines and phantom nodes, demonstrating high efficiency through test examples.

Contribution

It introduces a phantom node method for trigonometric spline interpolation that effectively eliminates gaps in functions and derivatives.

Findings

High efficiency demonstrated on test examples

Effective gap elimination in function and derivatives

Applicable to periodic functions on finite intervals

Abstract

Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate function with an even number of values of a phantom function, which is constructed in such a way as to eliminate gaps in both the function itself and its derivatives up to and including a certain order; in the General case, these gaps occur with the periodic continuation of the function given at a finite interval. The results of calculations on test examples for trigonometric splines of the third order are given; these calculations illustrate the high efficiency of the proposed method.