A symmetric matrix $A\in \Bbb{R}^{n\times n}$ is copositive if for every vector $x\in\Bbb{R}^n$ with non-negative entries, we have $$x^TAx \ge 0.$$
What are known methods to check if a specific matrix $A$ is copositive that are efficient in practice? I'm looking for something which will return an answer for a single instance of a 48x48 matrix in at most a week. I also wish for the implementation to not give false positive due to floating-errors, so I guess I am looking for a quadratic programming method which keeps track of its numerical precision/error bounds.
I have skimmed through this article: A Variational Approach to Copositive Matrices. While it details various methods to check if a matrix is copositive, I am not too familiar with matrix algorithms and could not determine what the expected run times of these methods would be.
