Box splines with rational directions and linear diophantine equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)270-277
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume203
Issue number1
Publication statusPublished - 1 Oct 1996
Externally publishedYes

Abstract

A necessary and sufficient condition for the linear independence of integer translates of Box splines with rational directions is presented in terms of intrinsic properties of the defining matrices. We also give a necessary and sufficient condition for the space of linear dependence relations to be finite dimensional. A method to compute the approximation order of these Box spline spaces is obtained. All these conditions can be tested by finite steps of computations based on elementary properties of the matrices. The method of proofs is from linear diophantine equations. © 1996 Academic Press, Inc.