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 R 2 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.
Bounds for anisotropic kernels and the derivatives of the interpolant are developed in REF .
Error bounds for anisotropic RBF interpolation
J. Approx. Theory
J. Approx. Theory
Computer Science Mathematics