$h$-Trigonometric B-splines
Numerical Analysis
2025-08-07 v1 Numerical Analysis
Abstract
We introduce discrete analogues of the exponential, sine, and cosine functions. Then using a discrete trigonometric version of a non-polynomial divided difference, we define discrete analogues of the trigonometric B-splines. We derive a two-term recurrence relation, a two-term formula for the discrete derivative, and two variants of the Marsden identity for these discrete trigonometric B-splines. Since the classical exponential, sine, and cosine functions are limiting cases of their discrete analogues, we conclude that many of the standard results for classical polynomial B-splines extend naturally both to trigonometric B-splines and to discrete trigonometric B-splines.
Cite
@article{arxiv.2508.04582,
title = {$h$-Trigonometric B-splines},
author = {Fatma Zürnacı-Yetiş and Ron Goldman and Plamen Simeonov},
journal= {arXiv preprint arXiv:2508.04582},
year = {2025}
}