Error bounds for anisotropic RBF interpolation

R. Beatson, O. Davydov, J. Levesley, EPSRC (grant EP/F009615) (Funder)

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13 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)512-527
Number of pages16
JournalJournal of Approximation Theory
Volume162
Issue number3
DOIs
Publication statusPublished - Mar 2010

Keywords

  • radial basis functions
  • anisotropic approximation

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    Beatson, R., Davydov, O., Levesley, J., & EPSRC (grant EP/F009615) (Funder) (2010). Error bounds for anisotropic RBF interpolation. Journal of Approximation Theory, 162(3), 512-527. https://doi.org/10.1016/j.jat.2009.08.004