Error bounds for anisotropic RBF interpolation

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R2 we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centres are anisotropic, and this improvement is confirmed numerically.

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Richard K. Beatson, Oleg Davydov, Jeremy Levesley
• Keywords: Growth Function, JAT 2010, Polyharmonic Basic Functions, Radial Basis Functions