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

Gülter Budakçı ^[1] ; Çetin Dişibüyük ^[1] ; Ron Goldman ^[2] ; Halil Oruç ^[1]
1. [1] Dokuz Eylül University
  
  Dokuz Eylül University
  
  Turquía
2. [2] Rice University
  
  Rice University
  
  Estados Unidos
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 282, Nº 1 (July 2015), 2015, págs. 17-33
Idioma: inglés
DOI: 10.1016/j.cam.2014.12.034
Enlaces
- Texto completo
Resumen
- 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/q1/q-convolution formula for uniform qq-B-splines.