### Convergence of polyharmonic splines on semi-regular grids Z x aZ^n for a to 0

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Title: | Convergence of polyharmonic splines on semi-regular grids Z x aZ^n for a to 0 |

Authors: | Kounchev, Ognyan Render, Hermann |

Permanent link: | http://hdl.handle.net/10197/5510 |

Date: | Jul-2007 |

Abstract: | Let p,n ∈ N with 2 p ≥ n + 2 , and let I a be a polyharmonic spline of order p on the grid Z × a Z n which satisfies the interpolating conditions I a ( j,am ) = d j ( am ) for j ∈ Z ,m ∈ Z n where the functions d j : R n → R and the parameter a> 0 are given. Let B s ( R n ) be the set of all integrable functions f : R n → C such that the integral k f k s := Z R n b f ( ξ ) (1 + | ξ | s ) dξ is finite. The main result states that for given σ ≥ 0 there exists a constant c> 0 such that whenever d j ∈ B 2 p ( R n ) ∩ C ( R n ) ,j ∈ Z , satisfy k d j k 2 p ≤ D · (1 + | j | σ ) for all j ∈ Z there exists a polyspline S : R n +1 → C of order p on strips such that | S ( t,y ) − I a ( t,y ) |≤ a 2 p − 1 c · D · (1 + | t | σ ) for all y ∈ R n ,t ∈ R and all 0 <a ≤ 1. |

Type of material: | Journal Article |

Publisher: | Springer |

Copyright (published version): | 2007 Springer |

Keywords: | Radial basis functions;Interpolation;Polysplines;Poly- harmonic splines |

DOI: | 10.1007/s11075-007-9099-x |

Language: | en |

Status of Item: | Peer reviewed |

Appears in Collections: | Mathematics and Statistics Research Collection |

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