Non-polynomial divided differences and B-spline functions

Zürnacı Yetiş F., Dişibüyük Ç.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 349
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.cam.2018.09.026
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.579-592
  • Anahtar Kelimeler: Divided differences, Non-polynomial divided differences, Generalized Hermite interpolation, B-spline
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.