非奇异H-矩阵新的充分条件  

New Sufficient Conditions for Nonsingular H-matrices

作　　者：王明刚[1] 宋岱才[1] 田秋菊[1] 

机构地区：[1]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《四川师范大学学报（自然科学版）》2011年第3期300-304,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：辽宁省教育厅高校科研基金(2004F100)资助项目

摘　　要：在数值线性代数的理论和应用中,H-矩阵是一类非常重要的矩阵.设A=(aij)∈Cn×n,若存在α∈(0,1),使i∈N,|aii|≥Riα(A)S1i-α(A),则称A为α-链对角占优矩阵.首先推广α-链对角占优矩阵的概念到广义α-链对角占优矩阵,通过利用α-链对角占优矩阵的性质,结合不等式的放缩技巧,给出了判别非奇异H-矩阵新的充分条件,改进和推广了相关文献的结论.最后用数值例子说明了所给结果的优越性.In the theory and applications of numerical linear algebra,the class of H-matrices is very important.Let A=（aij）∈Cn×n,if there exists α∈（0,1） which can make ｜aii｜≥Rαi（A）S1-αi（A） be right for i∈N,then A is called an α-chain diagonally dominant matrix.In this paper,the concept is extended to that of generalized α-chain diagonally dominant matrices.By using the properties of α-chain diagonally dominant matrices and applying some techniques of inequalities,some new sufficient conditions for a matrix to be a nonsingular H-matrix are obtained.The results obtained improve the known corresponding results.At last a numerical example is given for illustrating the advantage of our results.

关 键 词：α-链对角占优矩阵 不可约矩阵 非奇异H-矩阵 

分 类 号：O151.21[理学—数学]