Error estimates for interpolation of rough data using the scattered shifts of a radial basis function
- 56 Downloads
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in Rd, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function – the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.
Keywordsscattered data interpolation radial basis functions error estimates rough functions
Unable to display preview. Download preview PDF.
- R. Brownlee and J. Levesley, A scale of improved error estimates for radial approximation in Euclidean space and on spheres, Math. Comp. (2004) submitted. Google Scholar
- R. Brownlee and W. Light, Approximation orders for interpolation by surface splines to rough functions, IMA J. Numer. Anal. 24(2) (2004) 179–192. Google Scholar
- G.J.O. Jameson, Topology and Normed Spaces (Chapman and Hall, London, UK, 1974). Google Scholar
- J. Levesley and W.A. Light, Direct form seminorms arising in the theory of interpolation by translates of a basis function, Adv. Comput. Math. 11(2–3) (1999) 161–182. Google Scholar
- W.A. Light and M.L. Vail, Extension theorems for spaces arising from approximation by translates of a basic function, J. Approx. Theory 114(2) (2002) 164–200. Google Scholar
- F.J. Narcowich and J.D. Ward, Scattered-data interpolation on Rn: Error estimates for radial basis and band-limited functions, SIAM J. Math. Anal. 36 (2004) 284–300. Google Scholar
- F.J. Narcowich, J.D. Ward and H. Wendland, Sobolev bounds on functions with scattered zeros with application to radial basis function surface fitting, Math. Comp. to appear. Google Scholar
- J. Yoon, Interpolation by radial basis functions on Sobolev space, J. Approx. Theory 112(1) (2001) 1–15. Google Scholar