中文摘要：

推广α-对角占优矩阵的概念到广义α-对角占优矩阵,利用这一概念和不等式的缩放加技巧,最后得到了判别非奇异H-矩阵的一个判定方法,从而使得对α-对角占优矩阵和H-矩阵的判定问题在实际应用中更加简便而有效.

英文摘要：

Concept ofα-diagonally dominant matrix is extended to generalizedα-diagonally dominant matrix,which is together with zoom technique of inequality used to obtain a new criterin for nonsingular H-matrix.This method makes the criterion for generalizedα-diagonally dominant matrices and H-matrices simpler and more effertive more in practice.