非奇H-矩阵的两个子类

Two Subsets of Nonsingular H-Matrix

给出局部(α,β)-双对角占优矩阵的相关概念。对于给定的复矩阵A,在严格局部(α,β)-双对角占优及不可约局部(α,β)-双对角占优矩阵的条件下,通过建立合适的正对角阵X,得出B=AX为严格α-对角占优矩阵或不可约α-对角占优矩阵,从而获得了A为非奇异H-矩阵的两个实用判别准则。所得结果表明,提出这种延伸的局部(α,β)-双对角占优矩阵的概念,是对矩阵的对角占优理论的完善,是研究H-矩阵、M-矩阵的有力工具。这不仅促进了矩阵理论本身的发展,而且为计算数学、控制论等相关领域的研究奠定了更加坚实的基础。

The concept of local （α,β） - doubly diagonally dominant matrix was introduced, Under the conditions of strict local （α,β） -doubly diagonally dominant and irreducible local （α,β） - doubly diagonally dominant matrix, the conclusion that B = AX is a strict α - diagonally dominant matrix or irreducible α - diagonally dominant matrix was presented by constructing a suitable positive diagonal matrix X, for a given complex matrix A, thus two practical criterions of nonsingular H - matrix were obtained. The results show that the extended local （α,β） - doubly diagonally dominant concept is a development for matrix＇s doubly diagonally dominance＇ s theory and a powerful tool for re.arching of H - matrix and M - matrix, These conclusions not only promote the development of matrix＇s theory itself, but also provide strong basis for the research of relative fields such as computational mathematic, control theory, etc.