Error bounds for anisotropic RBF interpolation

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

doi:10.1016/j.jat.2009.08.004

Error bounds for anisotropic RBF interpolation

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

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	512-527
Number of pages	16
Journal	Journal of Approximation Theory
Volume	162
Issue number	3
DOIs	https://doi.org/10.1016/j.jat.2009.08.004
Publication status	Published - Mar 2010

Keywords

radial basis functions
anisotropic approximation

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10.1016/j.jat.2009.08.004

Cite this

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title = "Error bounds for anisotropic RBF interpolation",

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.",

keywords = "radial basis functions, anisotropic approximation",

author = "R. Beatson and O. Davydov and J. Levesley and {EPSRC (grant EP/F009615) (Funder)}",

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AU - Beatson, R.

AU - Davydov, O.

AU - Levesley, J.

AU - EPSRC (grant EP/F009615) (Funder)

PY - 2010/3

Y1 - 2010/3

N2 - 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.

AB - 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.

KW - radial basis functions

KW - anisotropic approximation

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EP - 527

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 3

ER -

Error bounds for anisotropic RBF interpolation

Abstract

Keywords

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Other files and links

Efficient computation with radial basis functions

Cite this

Error bounds for anisotropic RBF interpolation

Abstract

Keywords

Access to Document

Other files and links

Projects

Efficient computation with radial basis functions

Cite this