Optimal Lagrange interpolation by quartic C1 splines on triangulations
| Autor: | Frank Zeilfelder, Gero Hecklin, Charles K. Chui, Günther Nürnberger |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Applied Mathematics
MathematicsofComputing_NUMERICALANALYSIS Lagrange polynomial Bilinear interpolation Stairstep interpolation Computer Science::Computational Geometry Combinatorics Computational Mathematics symbols.namesake Nearest-neighbor interpolation TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Calculus Bicubic interpolation Spline interpolation ComputingMethodologies_COMPUTERGRAPHICS Trigonometric interpolation Mathematics Interpolation |
| Zdroj: | Journal of Computational and Applied Mathematics. 216:344-363 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2007.05.013 |
| Popis: | We develop a local Lagrange interpolation scheme for quartic C^1 splines on triangulations. Given an arbitrary triangulation @D, we decompose @D into pairs of neighboring triangles and add ''diagonals'' to some of these pairs. Only in exceptional cases, a few triangles are split. Based on this simple refinement of @D, we describe an algorithm for constructing Lagrange interpolation points such that the interpolation method is local, stable and has optimal approximation order. The complexity for computing the interpolating splines is linear in the number of triangles. For the local Lagrange interpolation methods known in the literature, about half of the triangles have to be split. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect