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

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.

minor revision, two new references; Conference Proceedings: Curves and Surfaces 2014, J.-D.Boissonnat et al. (Eds.), Springer, LNCS 9213, 2015

References in corpus (2)

• Transfinite thin plate spline interpolation
• Radially symmetric thin plate splines interpolating a circular contour map

Cited by in corpus (1)

• Radially symmetric thin plate splines interpolating a circular contour map