Local Lagrange Interpolation with Bivariate Splines of Arbitrary Smoothness |
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Authors: | Günther Nürnberger Vera Rayevskaya Larry L Schumaker Frank Zeilfelder |
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Institution: | (1) Institute for Mathematics, University of Mannheim, 68131 Mannheim , Germany;(2) Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA;(3) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
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Abstract: | We describe a method which can be used to interpolate
function values at a set of 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 some 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. |
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Keywords: | Bivariate interpolation Splines |
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