块严格局部双对角占优矩阵及其逆的无穷大范数的上界

The Upper Bound of the Infinite Norm of a Block Strictly Locally Doubly Diagonally Dominant Matrix and Its Inverse

摘要: 本文研究了块H-矩阵的一个新子类——块严格局部双对角占优矩阵的性质及应用，给出了块H-矩阵的新判据。同时分析了该矩阵与块H-矩阵的其它子类的关系，并给出了其逆矩阵的无穷大范数上界的估计式。数值算例表明，本文所得结论在一定程度上优于现有的定理结果。

Abstract: This paper studies the properties and applications of a new subclass of the block H-matrices—block strictly locally doubly diagonally dominant matrices, and presents a new criterion for block H-matrices. Meanwhile, the relationship between this matrix and other subclasses of the block H-matrix was analyzed, and the estimation formula of the upper bound of the infinite norm of its inverse matrix was given. Numerical examples show that the conclusions obtained in this paper are superior to the existing theorem results to a certain extent.