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- Title
The Cone of 5×5 Completely Positive Matrices.
- Authors
Pfeffer, Max; Samper, José Alejandro
- Abstract
We study the cone of completely positive (cp) matrices for the first interesting case n = 5 . This is a semialgebraic set for which the polynomial equalities and inequlities that define its boundary can be derived. We characterize the different loci of this boundary and we examine the two open sets with cp-rank 5 or 6. A numerical algorithm is presented that is fast and able to compute the cp-factorization even for matrices in the boundary. With our results, many new example cases can be produced and several insightful numerical experiments are performed that illustrate the difficulty of the cp-factorization problem.
- Subjects
SEMIALGEBRAIC sets; MATRICES (Mathematics); CONES; ALGEBRAIC geometry; CONVEX geometry; FACTORIZATION
- Publication
Discrete & Computational Geometry, 2024, Vol 71, Issue 2, p442
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-023-00620-y