About the classification of trigonometric splines

TL;DR

This paper proposes a classification scheme for trigonometric interpolation splines based on convergence factors, basis function signs, and interpolation factors, introducing concepts of crosslinking and interpolation grids with illustrative examples.

Contribution

It introduces a new classification framework for trigonometric splines, including the concepts of crosslinking and interpolation grids, with practical illustration.

Findings

Classification depends on convergence factors and basis function signs

Introduction of crosslinking and interpolation grid concepts

Illustrative example demonstrating the classification

Abstract

One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The concept of crosslinking and interpolation grids is introduced; these grids can either match or not match. The proposed classification is illustrated by an example.