Error Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree

✍ Scribed by Holger Wendland

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 255 KB
• Volume: 93
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1997.3137

✦ Synopsis

We consider error estimates for interpolation by a special class of compactly supported radial basis functions. These functions consist of a univariate polynomial within their support and are of minimal degree depending on space dimension and smoothness. Their associated ``native'' Hilbert spaces are shown to be normequivalent to Sobolev spaces. Thus we can derive approximation orders for functions from Sobolev spaces which are comparable to those of thin-plate-spline interpolation. Finally, we investigate the numerical stability of the interpolation process.

1998 Academic Press

A large number of centers x j on the one hand or a large number of evaluations of the interpolating function (1) on the other hand makes it obviously desirable to have a compactly supported basis function 8 of the simplest possible form. But the most popular 8's are not compactly supported. They often do not even allow one to form the interpolant as a pure ``radial'' sum (1), so Article No. AT973137 258