How to Obtain a Lattice Basis from a Discrete Projected Space

  • Nicolas Normand
  • Myriam Servières
  • JeanPierre Guédon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)


Euclidean spaces of dimension n are characterized in discrete spaces by the choice of lattices. The goal of this paper is to provide a simple algorithm finding a lattice onto subspaces of lower dimensions onto which these discrete spaces are projected. This first obtained by depicting a tile in a space of dimension n – 1 when starting from an hypercubic grid in dimension n. Iterating this process across dimensions gives the final result.


Projection Matrix Discrete Space Riesz Basis Projection Direction Continuous Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nicolas Normand
    • 1
  • Myriam Servières
    • 1
  • JeanPierre Guédon
    • 1
  1. 1.IRCCyN/IVC, École polytechniqueUniversity of NantesNantes

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