Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Node Optimization via Partial Fluctuation Suppression


GÜRVİT E. , Baykara N. A.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Rhodes, Yunanistan, 22 - 28 Eylül 2014, cilt.1648 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1648
  • Doi Numarası: 10.1063/1.4912457
  • Basıldığı Şehir: Rhodes
  • Basıldığı Ülke: Yunanistan

Özet

This work's content finds its root in the material given in the first three companion papers on the very newly proposed method called "Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions". Those three and the present companion papers are to appear in this proceedings. This work focuses on the determination of the nodal values which make the Euclidean distance between the target function and the SNADE truncation polynomial under consideration. The minimization procedure uses certain elements of the mathematical fluctuation theory. We obtain nonlinear equations after the minimization of the Euclidean distance mentioned above. The solutions of these equations can be numerically obtained unless the target function has a very specific structure. This is a so-called "baby age" theory and needs very specific care for robustness and sophistication. Here, the purpose is just formalism and conceptuality. Practicality has been left to future works.