Non-polynomial divided difference and blossoming
Numerical Analysis
2026-03-18 v2 Numerical Analysis
Abstract
Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities. Moreover, the divided differences of polynomials can be expressed in terms of the blossom. In this paper, an extended non-polynomial homogeneous blossom for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special M\"{u}ntz spaces of splines, is defined. It is shown that there is a relation between the non-polynomial divided difference and the blossom, which is analogous to the polynomial case.
Cite
@article{arxiv.2512.21891,
title = {Non-polynomial divided difference and blossoming},
author = {Fatma Zürnacı-Yetiş},
journal= {arXiv preprint arXiv:2512.21891},
year = {2026}
}