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Thin plate splines for transfinite interpolation at concentric circles

Abstract

We propose a new method for constructing a polyspline on annuli, i.e. a C 2 surface on ℝ2 \ {0}, which is piecewise biharmonic on annuli centered at 0 and interpolates smooth data at all interface circles. A unique surface is obtained by imposing Beppo Levi conditions on the innermost and outermost annuli, and one additional restriction at 0: either prescribing an extra data value, or asking that the surface is non-singular. We show that the resulting Beppo Levi polysplines on annuli are in fact thin plate splines, i.e. they minimize Duchon's bending energy.

Keyword : approximation, interpolation, spline

How to Cite
Bejancu, A. (2013). Thin plate splines for transfinite interpolation at concentric circles. Mathematical Modelling and Analysis, 18(3), 446-460. https://doi.org/10.3846/13926292.2013.807317
Published in Issue
Jun 1, 2013
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This work is licensed under a Creative Commons Attribution 4.0 International License.