非奇异H-矩阵的一组新判定方法

A Set of New Criterion for Judging Nonsingular H-matrices

非奇异H-矩阵在控制理论、科学计算和工程应用中具有重要的作用,但在实际中要判定一给定矩阵为非奇异H-矩阵是有难度的.本文通过研究给定矩阵元素的性质,对矩阵元素的航标集进行分割,巧妙地构造正对角矩阵和运用不等式的放缩方法,给出了非奇异H-矩阵的一组新的实用性新判定方法.进一步,将相关结果推广到不可约和具有非零元素链的情形.最后,我们改进和推广了相关的结果,并举例说明了所得方法的优越性.

Nonsingular H-matrix plays a significant role in the control theory, the scientific computation and the applications in engineering. However, it is difficult to specify a non- singular H-matrix in practice. In this paper, we partition the row index set by studying the elements of a matrix, and construct a positive diagonal matrix. Then, we apply some techniques in inequalities to obtain a new criterion for nonsingular H-matrices. We also obtain several similar results in the cases of irreducible matrices and matrices with non-zero elements chains. These consequences improve and generalize the related results, and the advantage of the proposed consequences are illustrated by several numerical examples.