Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 41A05, 41A15, 41A25, 41A30, 41A63

Retrieve articles in all journals with MSC (2000): 41A05, 41A15, 41A25, 41A30, 41A63

Additional Information

Jungho Yoon
Affiliation: Department of Mathematics, Ewha Women’s University, Dae Hyun-Dong, Seo Dae Moon-Gu, Seoul 120-750, Korea

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