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Research Report MRR00-032
Approximation of a Thin Plate Spline Smoother using Continuous Piecewise
Polynomial Functions
Stephen Roberts, Markus Hegland and Irfan Altas
Abstract:
In this work, a new smoothing method is proposed which can be viewed as a
discrete thin plate spline. This new approach combines the favourable
properties of finite element surface fitting with the ones of thin plate
splines. The method is based on first order techniques similar to mixed
finite element techniques for the biharmonic equation. The existence of a
solution to our smoothing problem is demonstrated and the approximation
theory for uniformly spread data is presented. Numerical results
verifying our theoretical results and demonstrating our method on a large
real life data sets are presented.
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