广义双对角占优矩阵的Schur余

The Schur Complements of Generalized Doubly Diagonally Dominant Matrices

我们知道对角占优矩阵的Schur余是对角占优矩阵,对于双对角占优矩阵也有这样的性质,这种性质也可以推广到严格广义双对角占优矩阵的情况。本文研究了非严格广义双对角占优矩阵的Schur余,给出了广义双对角占优矩阵的Schur余仍可保持对角优势的特性。

The Schur complements of diagonally dominant matrices are diagonally dominant and the same is true for strictly doubly diagonally dominant matrices. These results may also be extended to the generalized strictly doubly diagonally dominant matrices. The purpose of this paper is to extend the above result to generalized doubly diagonally dominant matrices, that is, we show the Schur complement of a generalized doubly diagonally dominant matrix is also a diagonally dominant matrix under some conditions.