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

Budakçı G., Dişibüyük Ç., Goldman R., Oruç H.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.282, ss.17-33, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 282
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.cam.2014.12.034
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.17-33
  • Anahtar Kelimeler: Quantum splines, q-B-splines, h-B-splines, Divided differences, Quantum derivatives, Quantum integrals, DISCRETE SPLINES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.