On the stationary Lp -approximation power to derivatives by radial basis function interpolation

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Abstract

In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say Cφ. However, if a basis function φ is smooth, the space Cφ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.

Original languageEnglish
Pages (from-to)875-887
Number of pages13
JournalApplied Mathematics and Computation
Volume150
Issue number3
DOIs
StatePublished - 17 Mar 2004

Bibliographical note

Funding Information:
This work was supported by Korea Research Foundation Grant (KRF-2003-C00014).

Keywords

  • 'Shifted' surface spline
  • Approximation power
  • Homogeneous Sobolev space
  • Interpolation
  • Multiquadric
  • Radial basis function

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