Extending fundamental formulas from classical B-splines to quantum B-splines

被引：13

作者：

Budakci, Gulter ^{[1
]}

Disibuyuk, Cetin ^{[2
]}

Goldman, Ron ^{[3
]}

Oruc, Halil ^{[2
]}

机构：

[1] Dokuz Eylul Univ, Dept Math, Fen Bilimleri Enstitusu, TR-35160 Izmir, Turkey

[2] Dokuz Eylul Univ, Dept Math, Fen Fak, TR-35160 Izmir, Turkey

[3] Rice Univ, Dept Comp Sci, Houston, TX 77251 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 282卷

关键词：

Quantum splines; q-B-splines; h-B-splines; Divided differences; Quantum derivatives; Quantum integrals; DISCRETE SPLINES;

D O I：

10.1016/j.cam.2014.12.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive a collection of fundamental formulas for quantum B-splines analogous to known fundamental formulas for classical B-splines. Starting from known recursive formulas for evaluation and quantum differentiation along with quantum analogues of the Marsden identity, we derive quantum analogues of the de Boor Fix formula for the dual functionals, explicit formulas for the quantum B-splines in terms of divided differences of truncated power functions, formulas for computing divided differences of arbitrary functions by quantum integrating certain quantum derivatives of these functions with respect to the quantum B-splines, closed formulas for the quantum integral of the quantum B-splines over their support, and finally a 1/q-convolution formula for uniform g-B-splines. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：17 / 33

页数：17