TITLE

Local Lagrange Interpolation with Bivariate Splines of Arbitrary Smoothness

AUTHOR(S)
Nürbberger, Günther; Rayevskaya, Vera; Schumaker, Larry L.; Zeilfelder, Frank
PUB. DATE
December 2005
SOURCE
Constructive Approximation;Nov2005, Vol. 23 Issue 1, p33
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We describe a method which can be used lo interpolate function values at a set ot scattered points in a planar domain using bivariate polynomial splines of any prescribed smoothness. The method starts with an arbitrary given triangulation of the data points, and involves refining sonic of the triangles with Clough-Tocher splits. The construction of the interpolating splines requires some additional function values at selected points in the domain, but no derivatives are needed at any point. Given n data points and a corresponding initial triangulation. the interpolating spline can be computed in just O(n) operations. The interpolation method is local and stable, and provides optimal order approximation of smooth functions,
ACCESSION #
19138637

 

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