偕正矩阵的判定  

CRITERIA FOR COPOSITIVE MATRICES

作　　者：李小新[1] 杨尚俊[2] 

机构地区：[1]池州学院数学系,池州247000 [2]安徽大学数学与计算科学学院,合肥230039

出　　处：《高等学校计算数学学报》2010年第1期37-46,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：安徽省高校青年教师科研基金资助项目(2007jql188);池州学院重点课题基金资助项目(2006XK06)

摘　　要：1引言与背景知识本文中,我们用A≥0(>0)表示A是非负(正)矩阵(向量).若没有特殊说明,以下所讨论的矩阵(向量)都是n阶实对称矩阵(n维实向量).定义1对称矩阵A称为偕正的(copositive)。The copositive matrices are very important in both research and application of matrix theory. This kind of matrices often occur in optimization theory. Recently many papers researched ways of determining whether a given symmetric matrix is copositive. As the general problem of testing for copositivity is NPcomplete, it is very difficult to obtain a simple and efficient way. In this paper, we give some conditions to test whether a symmetric matrix of order n ≤9 is copositive in terms of simplex theory. It is easy to give, from our results, the corre- sponding algorithms for determining the copositivity of a given symmetric matrix. We made MATLAB programming for these algorithms and found that they work quite well.

关 键 词：COPOSITIVE strictly copositive symmetric matrices SIMPLEX 

分 类 号：O151.2[理学—数学]