α-双对角占优矩阵的等价表征及应用

Equivalent Representation of α-Double Diagonally Dominant Matrices and Its Application

依据对角占优矩阵理论和α-对角占优矩阵之间的关系,给出严格α1-双对角占优矩阵的等价表征,由此得到一个非奇异H-矩阵的判定准则,并给出判定非奇异H-矩阵的算法及程序,最后通过数值结果说明了判定方法的有效性.

According to the relations of the theory of diagonally dominant matrices and diagonally dominant matrices,an equivalent representation for strictly α1-double diagonally dominant matrices is given.By using the equivalent condition,a criterion for nonsingular H-matrices is obtained.At the same time,an algorithm and corresponding program for distinguishing nonsingular H-matrices is given.In the end,several numerical examples are carried out to show the efficiency of the proposed criteria.