非奇异H-矩阵的新判据  

New Criteria for Nonsingular H-matrices

作　　者：江如[1] 

机构地区：[1]广东海洋大学理学院,湛江524088

出　　处：《工程数学学报》2011年第3期393-400,共8页Chinese Journal of Engineering Mathematics

摘　　要：非奇异H-矩阵在矩阵分析和数值代数的研究中具有重要作用.本文利用广义α-对角占优矩阵、不可约α-对角占优矩阵和具非零元素链α-对角占优矩阵的概念和性质,通过对矩阵行标作划分的方法,首先给出了非奇异H-矩阵的两个新的判定条件.然后进一步将所得结果应用于比较矩阵和转置比较矩阵的和,得到了另一个更为实用的判据.最后,用数值例子说明了所给结果的有效性.Nonsingular H-matrices play an important role in the research of matrix analysis and numerical algebra.Based on the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and α-diagonally dominant matrices with a nonzero elements chain,two new criteria for nonsingular H-matrices are obtained firstly in this paper according to the partition of the row indices.Secondly,a more practical criterion is also obtained by applying the above results to the sum of the comparison matrix and its transpose.A numerical example is presented to illustrate the effectiveness of the presented criteria.

关 键 词：非奇异H-矩阵 比较矩阵 Α-对角占优矩阵 不可约矩阵 非零元素链 

分 类 号：O151.21[理学—数学]