Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 498631, 10 pages
Research Article

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

1School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
2School of Sciences, Zhejiang Forestry University, Hangzhou, ZheJiang 311300, China
3Department of Mathematics, Chizhou Institute, Chizhou, Anhui, China

Received 5 October 2009; Accepted 10 November 2009

Academic Editor: Shusen Ding

Copyright © 2010 Yang Shang-jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 n8 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.