A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix

• Main Authors: Yang Shang-jun, Xu Chang-qing, Li Xiao-xin
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://dx.doi.org/10.1155/2010/498631

In the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. The algorithms for matrices of order n≥8 are not guaranteed to produce an answer. It also shows that for 1000 symmetric random matrices of order 8, 9, and 10 with unit diagonal and with positive entries all being less than or equal to 1 and negative entries all being greater than or equal to −1, there are 8, 6, and 2 matrices remaing undetermined, respectively. In this paper we give two more algorithms for n=8,9 and our experiment shows that no such matrix of order 8 or 9 remains undetermined; and almost always no such matrix of order 10 remains undetermined. We also do some discussion based on our experimental results.