Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

Numerical Algorithms

Volumn 39, Issue 1-3, 2005, Pages 57-68

  Brownlee, R A ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Error estimates; Radial basis functions; Rough functions; Scattered data interpolation

Indexed keywords

EID: 17444399302     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11075-004-3620-2     Document Type: Article

References (10)

1. R. Brownlee and J. Levesley, A scale of improved error estimates for radial approximation in Euclidean space and on spheres, Math. Comp. (2004) submitted.
2. R. Brownlee and W. Light, Approximation orders for interpolation by surface splines to rough functions, IMA J. Numer. Anal. 24(2) (2004) 179-192.
3. G.J.O. Jameson, Topology and Normed Spaces (Chapman and Hall, London, UK, 1974).
4. 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.
5. 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.
6. W.A. Light and H. Wayne, Spaces of distributions, interpolation by translates of a basis function and error estimates, Numer. Math. 81(3) (1999) 415-450.
7. n: Error estimates for radial basis and band-limited functions, SIAM J. Math. Anal. 36 (2004) 284-300.
8. 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.
9. J. Yoon, Interpolation by radial basis functions on Sobolev space, J. Approx. Theory 112(1) (2001) 1-15.
10. p-error estimates for "shifted" surface spline interpolation on Sobolev space, Math. Comp. 72(243) (2003) 1349-1367 (electronic).