Box Splines pp 137-158 | Cite as

Discrete box splines & linear diophantine equations

  • Carl de Boor
  • Klaus Höllig
  • Sherman Riemenschneider
Part of the Applied Mathematical Sciences book series (AMS, volume 98)


In this chapter, we give the basic properties of the discrete box spline, in close analogy to those of the (continuous) box spline discussed in Chapter I. This includes facts about the structure of the discrete box spline, as well as the characterization of global and local linear independence. This gives us a chance to stress the perhaps surprising connection between box splines and linear diophantine equations.


Full Rank Integer Solution Linear Independence Integer Matrix Uniform Scaling 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Carl de Boor
    • 1
  • Klaus Höllig
    • 2
  • Sherman Riemenschneider
    • 3
  1. 1.Center for Mathematical SciencesUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Math Institut A der UniversitätStuttgart 80Germany
  3. 3.Department of MathematicsUniversity of AlbertaEdmontonCanada

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