非奇H-矩阵的一组迭代判别法  

A GROUP OF NEW ITERATIVE CRITERIA FOR NONSINGULAR H-MATRICES

作　　者：李玲[1] 徐仲[1] 陆全[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《数值计算与计算机应用》2015年第2期91-99,共9页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(10802068)资助项目

摘　　要：非奇异H-矩阵在数值线性代数的理论与应用中起着重要作用,因此判定一个矩阵是否为非奇异H-矩阵有着非常重要的意义.本文根据广义严格α-链对角占优矩阵和广义严格α-对角占优矩阵的性质,以及引入迭代因子,给出了一组非奇异H-矩阵新的迭代判定条件.这些判定条件推广和改进了相关已有结果,丰富和完善了非奇异H-矩阵的理论,数值算例说明了其有效性.Since nonsingular H-matrices play important roles in the theory and application of Numerical Linear Algebra, it is necessary to know whether a given matrix is a nonsingular H-matrix. In this paper, a group of some sufficient conditions for nonsingular H-matrices is given according to the properties of generalized strictly α-chain diagonally dominant matrices, generalized strictly α- diagonally dominant matrices, and the method of applying the iteration factors. In addition, it improves some related results and enriches the theory of nonsingular H-matrices. Finally, the effectiveness of these sufficient conditions is illustrated with numerical examples.

关 键 词：广义严格α-链对角占优矩阵 广义严格α-对角占优矩阵 非奇异H-矩阵 迭代因子 

分 类 号：O241.6[理学—计算数学]