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 ∈ 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 ∈ C * or converges to a matrixS in C * which in some sense is "close" to B. Numerical experiments on matrices B of dimension up to 200 conclude the presentation.

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