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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