Non-polynomial divided differences and B-spline functions


Zurnaci F., Disibuyuk C.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.349, pp.579-592, 2019 (SCI-Expanded) identifier identifier

Abstract

Starting with the interpolation problem, we define non-polynomial divided differences recursively as a generalization of classical divided differences. We also derive the identities and the properties of these non-polynomial divided differences such as symmetry and Leibniz formula which is a main tool in the derivation of B-spline recurrence relations. Defining a novel variant of the truncated power function, we express non-polynomial B-splines explicitly in terms of non-polynomial divided differences of this truncated power function. (C) 2018 Elsevier B.V. All rights reserved.