An Upper Dimension Bound of the Pre-Kernel

  • Holger Ingmar Meinhardt
Part of the Theory and Decision Library C book series (TDLC, volume 45)


The dual representation of the pre-kernel enables us to provide a simple upper dimension bound formula on the pre-kernel set. This upper bound is equal to n − 3, from which we can finally determine a refined assignment on the maximum number of iteration steps required to successfully terminate a pre-kernel search process. At most \(\binom{n}{2} - 1\)-iteration steps are needed to single out a member of the pre-kernel under a regime of orthogonal projections.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Holger Ingmar Meinhardt
    • 1
  1. 1.Institute of Operations ResearchKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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