## Abstract

The present paper considers the approximation to a function and its derivatives by radial basis function interpolation and its derivatives respectively on the Sobolev space. It is known that due to edge effects, we lose some accuracy near the boundary. Thus, the goal of this paper is to show that the convergence rate of the approximation error can be at least doubled when a certain boundary condition is met.

Original language | English |
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Pages (from-to) | 109-119 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 161 |

Issue number | 1 |

DOIs | |

State | Published - 4 Feb 2005 |

### Bibliographical note

Funding Information:This work was supported by the Korea Research Foundation Grant of KRF-2003-003-C00015.

## Keywords

- Interpolation
- Multiquadric
- Radial basis function
- Shifted surface spline
- Sobolev space

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