On computing derivatives forC 1 interpolating schemes: an optimization |
| |
Authors: | S. De Marchi |
| |
Affiliation: | (1) Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze, 206 (Loc. Rizzi), 33100 Udine, Italy |
| |
Abstract: | The application of Powell-Sabin’s or Clough-Tocher’s schemes to scattered data problems, as known requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. We study alocal method for generating partial derivatives based on the minimization of the energy functional on the star of triangles sharing a node that we called acell. The functional is associated to some piecewise polynomial function interpolating the points. The proposed method combines theglobal Method II by Renka and Cline (cf. [16, pp. 230–231]) with the variational approach suggested by Alfeld (cf. [2]) with care to efficiency in the computations. The locality together with some implementation strategies produces a method well suited for the treatment of a big amount of data. An improvement of the estimates is also proposed. |
| |
Keywords: | 65D05 65D10 65D15 |
本文献已被 SpringerLink 等数据库收录! |
|