Error bounds for anisotropic RBF interpolation

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

Research output: Contribution to journalArticle

11 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.
LanguageEnglish
Pages512-527
Number of pages16
JournalJournal of Approximation Theory
Volume162
Issue number3
DOIs
Publication statusPublished - Mar 2010

Fingerprint

Error Bounds
Interpolation
Interpolate
Growth Function
Partial derivative
Approximation Error
Radial Functions
Placement
Basis Functions
Predict
Unknown
Target
Estimate
Derivatives

Keywords

  • radial basis functions
  • anisotropic approximation

Cite this

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
Beatson, R. ; Davydov, O. ; Levesley, J. ; EPSRC (grant EP/F009615) (Funder). / Error bounds for anisotropic RBF interpolation. In: Journal of Approximation Theory. 2010 ; Vol. 162, No. 3. pp. 512-527.
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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, vol. 162, no. 3, pp. 512-527. https://doi.org/10.1016/j.jat.2009.08.004

Error bounds for anisotropic RBF interpolation. / Beatson, R.; Davydov, O.; Levesley, J.; EPSRC (grant EP/F009615) (Funder).

In: Journal of Approximation Theory, Vol. 162, No. 3, 03.2010, p. 512-527.

Research output: Contribution to journalArticle

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