A simplex algorithm for rational cp-factorization

Mathieu Dutour Sikirić; Achill Schürmann; Frank Vallentin

doi:10.1007/s10107-020-01467-4

paper

A simplex algorithm for rational cp-factorization

arXiv:1807.01382 · doi:10.1007/s10107-020-01467-4

Abstract

In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cp-factorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be used to show that every integral completely positive $2 \times 2$ matrix has an integral cp-factorization.

(v4) 18 pages, some small corrections, to appear in Mathematical Programming