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Examples of linear multi-box splines

Part of: Numerical methods in Fourier analysis

Published online by Cambridge University Press:  01 December 2012

Abdellatif Bettayeb
Abdellatif Bettayeb*
Affiliation:
General Studies Department, Jubail Industrial College, PO Box 10099 Jubail industrial city 31961, Saudi Arabia (email: Bettayeb_a@jic.edu.sa, Abdellatif.bettayeb@gmail.com)

Abstract

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Let S1=S1(v0,…,vr+1) be the space of compactly supported C0 piecewise linear functions on a mesh M of lines through ℤ2 in directions v0,…,vr+1, possibly satisfying some restrictions on the jumps of the first order derivative. A sequence ϕ=(ϕ1,…,ϕr) of elements of S1 is called a multi-box spline if every element of S1 is a finite linear combination of shifts of (the components of) ϕ. We give some examples for multi-box splines and show that they are stable. It is further shown that any multi-box spline is not always symmetric

MSC classification

Secondary: 65T50: Discrete and fast Fourier transforms
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 444 - 462
Copyright
© The Author(s) 2012

References

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