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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

$L_p$-error estimates for ``shifted'' surface spline interpolation on Sobolev space


Author: Jungho Yoon
Journal: Math. Comp. 72 (2003), 1349-1367
MSC (2000): Primary 41A05, 41A15, 41A25, 41A30, 41A63
Published electronically: December 18, 2002
MathSciNet review: 1972740
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Abstract: The accuracy of interpolation by a radial basis function $\phi$ is usually very satisfactory provided that the approximant $f$ is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function $\phi$, no approximation power has yet been established. Hence, the purpose of this study is to discuss the $L_p$-approximation order ( $1\leq p\leq \infty$) of interpolation to functions in the Sobolev space $W^k_p(\Omega)$ with $k> \max(0,d/2-d/p)$. We are particularly interested in using the ``shifted'' surface spline, which actually includes the cases of the multiquadric and the surface spline. Moreover, we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met.


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Additional Information

Jungho Yoon
Affiliation: Department of Mathematics, Ewha Women’s University, Dae Hyun-Dong, Seo Dae Moon-Gu, Seoul 120-750, Korea
Email: yoon@math.ewha.ac.kr

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01498-9
PII: S 0025-5718(02)01498-9
Keywords: Radial basis function, interpolation, surface spline, ``shifted'' surface spline
Received by editor(s): April 4, 2000
Received by editor(s) in revised form: September 5, 2001
Published electronically: December 18, 2002
Article copyright: © Copyright 2002 American Mathematical Society