块H-矩阵的判定和应用

Criteria for Block H-Matrices and Its Application

利用矩阵的块对角占优和块广义严格对角占优的性质,给出了块严格α1-对角占优矩阵的等价表示,进而得到了块H-矩阵新的判定法则,即设A=(aij)∈Cn×n,M5=φ,若A满足‖Aii-1‖-1-Ri(A)/Ci(A)-Ri(A)+‖Ajj-1‖-1-Cj(A)/Rj(A)-Cj(A)≥1(i∈M1,j∈M2),则A为块H-矩阵。并应用于矩阵正稳定性的判定。

In this paper, based on the properties of block diagonal dominance and generalized strictly diagonal dominance matrices, the equivalent representations of block strictly al-diagonally dominant matrices are given. Furthermore, some criteria for block H-matrices are obtained, that is, let A=（aij）∈Cn×n,M5=φ,if A satisfies ‖Aii-1‖-1-Ri（A）/Ci（A）-Ri（A）＋‖Ajj-1‖-1-Cj（A）/Rj（A）-Cj（A）≥1（i∈M1,j∈M2）,then A is a block H-matrix. As their application, criteria for positive stability of matrices are given.