非奇异H-矩阵的新判定

APPLIED CRITERIA FOR NONSINGULAR H-MATRIX

应用广义严格对角占优矩阵的性质,对矩阵元素进行比较,确定了在一定区间范围内的数值因子,从而得到了一种判定非奇异H矩阵的新的方法.利用矩阵理论中不等式的方法和技巧,构造出相对应的正对角矩阵,并给出了严格的推导证明.由此推广得到了满足一定条件下的不可约矩阵以及具有非零元素链的矩阵,从而也得到了非奇异H矩阵的另外两种新的判定方法,最后用数值例子说明了结论的有效性.

A new criterion for nonsingular H-matrices is obtained firstly based on the properties of generalized strictly diagonally dominant matrices, comparing the elements of a matrix and ensuring the numerical divictor within limits. Strict proof is given using the methods and skills of inqualities in matrix theory, structuring correspondingly positive diagonal ma- trices. Additional two new criteria for nonsingular H-matrices are also obtained according to irreducible matrices and non-zero elements chain matrices satisfied controlled conditions. Effectiveness of the results is illustrated by the numerical examples.