On the computation of C* certificates

  • Florian Jarre
  • Katrin Schmallowsky


The cone of completely positive matrices C* is the convex hull of all symmetric rank-1-matrices xx T with nonnegative entries. While there exist simple certificates proving that a given matrix \({B\in C^*}\) is completely positive it is a rather difficult problem to find such a certificate. We examine a simple algorithm which—for a given input B—either determines a certificate proving that \({B\in C^*}\) or converges to a matrix \({\bar S}\) in C* which in some sense is “close” to B. Numerical experiments on matrices B of dimension up to 200 conclude the presentation.


Completely positive matrices 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversity of DüsseldorfDüsseldorfGermany

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