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The -approximation order of surface spline interpolation

Authors:	Michael J Johnson

Institution:	Deptartment of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait

Abstract:	We show that if the open, bounded domain $\Omega \subset \mathbb{R}^{d}$ has a sufficiently smooth boundary and if the data function is sufficiently smooth, then the $L_{p}(\Omega )$ -norm of the error between and its surface spline interpolant is $O(\delta ^{\gamma _{p}+1/2})$ ( $1\leq p\leq \infty$ ), where $\gamma _{p}:=\min \{m,m-d/2+d/p\}$ and is an integer parameter specifying the surface spline. In case , this lower bound on the approximation order agrees with a previously obtained upper bound, and so we conclude that the $L_{2}$ -approximation order of surface spline interpolation is .

Keywords:	Interpolation surface spline approximation order scattered data

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