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arXiv · 1411.1937

A new class of interpolatory $L$-splines with adjoint end conditions

Aurelian Bejancu·Reyouf S. Al-Sahli
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Abstract

A thin plate spline surface for interpolation of smooth transfinite data prescribed along concentric circles was recently proposed by Bejancu, using Kounchev's polyspline method. The construction of the new `Beppo Levi polyspline' surface reduces, via separation of variables, to that of a countable family of univariate $L$-splines, indexed by the frequency integer $k$. This paper establishes the existence, uniqueness and variational properties of the `Beppo Levi $L$-spline' schemes corresponding to non-zero frequencies $k$. In this case, the resulting $L$-spline end conditions are formulated in terms of \emph{adjoint} differential operators, unlike the usual `natural' $L$-spline end conditions, which employ identical operators at both ends. Our $L$-spline error analysis leads to an $L^{2}$-error bound for transfinite surface interpolation with Beppo Levi polysplines.

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Aurelian Bejancu, Reyouf S. Al-Sahli. 2014-11-07. A new class of interpolatory $L$-splines with adjoint end conditions. https://doi.org/10.1007/978-3-319-22804-4_3

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