## 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 C_{φ}. However, if a basis function φ is smooth, the space C_{φ} is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.

Original language | English |
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Pages (from-to) | 875-887 |

Number of pages | 13 |

Journal | Applied Mathematics and Computation |

Volume | 150 |

Issue number | 3 |

DOIs | |

State | Published - 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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