A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix. (28th December 2009)

• Record Type: Journal Article
• Authors: Shang-jun, Yang; Chang-qing, Xu; Xiao-xin, Li
• Other Names: Ding Shusen Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2010(2010)
• Publication Date: 2009-12-28
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2010/498631
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : 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 ordern ≥ 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 forn = 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.