广义α-双链对角占优矩阵的判定  

A criterion for generalized doubly α-chain diagonally dominant matrix

作　　者：王明刚[1] 宋岱才[1] 李金秋[1] 

机构地区：[1]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《纺织高校基础科学学报》2009年第3期284-287,共4页Basic Sciences Journal of Textile Universities

基　　金：辽宁省科学技术基金资助项目(001084);辽宁省教育厅高校科研项目(2004F100)

摘　　要：设A=(aij)∈Cn×n,若α∈(0,1),i,j∈N,i≠j,有|aii||ajj|≥Riα(A)Rjα(A)S1i-α(A)S1j-α(A)成立,则称A为α-双链对角占优矩阵.为给出H-矩阵的判别条件,首先推广α-双链对角占优矩阵到广义α-双链对角占优矩阵,然后得到了判别广义α-双链对角占优矩阵的一个充分条件,改进和推广了已有的结论,进一步丰富了广义α-双链对角占优矩阵和非奇H-矩阵的理论.LetA = （αij） ∈ C^n×n, if there exists α ∈（0, 1） which can make ｜aii｜｜ajj｜≥Riα（A）Rjα（A）S1i-α（A）S1j-α（A） be right for i,j∈N,i≠j, thenA is called a doubly at-chain diagonally dominant matrix. In order to obtain some simple determinate conditions for nonsingular H-matrix, the concept to generalized doubly at-chain diagonally dominant matrix was extended, the concept generalized doubly at-chain diagonally dominant matrix to obtain a new criteria condition was applied for a matrix to be a generalized doubly at-chain diagonally dominant matrix. The theory of doubly at-chain diagonally dominant matrix and nonsingular H-matrix are improved and completed.

关 键 词：广义α-双链对角占优矩阵 广义严格对角占优矩阵 H-矩阵 

分 类 号：O151.21[理学—数学]