Error bounds for anisotropic RBF interpolation

Beatson, R. and Davydov, O. and Levesley, J., EPSRC (grant EP/F009615) (Funder) (2010) Error bounds for anisotropic RBF interpolation. Journal of Approximation Theory, 162 (3). pp. 512-527. ISSN 0021-9045

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