Lagrange interpolation by bivariate \(C^1\)-splines with optimal approximation order
type: Item
instance of: scholarly article
title: Lagrange interpolation by bivariate \(C^1\)-splines with optimal approximation order
zbMATH Open document ID: 1064.41005
DOI: 10.1023/B:ACOM.0000032043.07621.62
author: Günther Nürnberger
author: Frank Zeilfelder
published in: Advances in Computational Mathematics
publication date: 2004-08-10T00:00:00Z
review text: The authors give a method of construction of local Lagrange interpolation points based on coloring methods for triangulations. This method consists of two steps: given an arbitrary triangulation A, in the first step they construct Lagrange interpolation points such that the interpolating spline is uniquely determined on the edges of A. Then, they use an algorithm that colors the triangles of A with two colors, black and white, and subdivide the white triangles by a Clough-Tocher split. In the second step, they choose Lagrange interpolation points such that the interpolating spline is determined in the black triangles. By choosing some further interpolation points the spline is determined on the whole triangulation. The resulting interpolation set includes all vertices of A. The interpolating splines yield optimal approximation order and can be computed with linear complexity.
reviewed by: Antonio López-Carmona
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 2085734
zbMATH Keywords: bivariate splines
zbMATH Keywords: Lagrange interpolation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2085734