R. Beatson, O. Davydov and J. Levesley, Error bounds for anisotropic RBF interpolation, J. Approx. Theory, 162 (2010), 512-527. DOI:10.1016/j.jat.2009.08.004

Abstract: 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 $\RR^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.

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