-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

DOI:
https://doi.org/10.1090/S0025-5718-02-01498-9

Published electronically:
December 18, 2002

MathSciNet review:
1972740

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Abstract | References | Similar Articles | Additional Information

Abstract: The accuracy of interpolation by a radial basis function is usually very satisfactory provided that the approximant is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function , no approximation power has yet been established. Hence, the purpose of this study is to discuss the -approximation order ( ) of interpolation to functions in the Sobolev space with . 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:
https://doi.org/10.1090/S0025-5718-02-01498-9

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