The Schur Complements of Generalized Doubly Diagonally Dominant Matrices
Linear Algebra and its Applications
Comparison matrix, Diagonally dominant matrix, Doubly diagonally dominant matrix, Generalized doubly diagonally dominant matrix, M-matrix, Schur complement
As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices (a proper subset of H-matrices); that is, we show that the Schur complement of a generalized doubly diagonally dominant matrix is a generalized doubly diagonally dominant matrix.
Liu, Jianzhou; Huang, Yunqing; and Zhang, Fuzhen, "The Schur Complements of Generalized Doubly Diagonally Dominant Matrices" (2004). Mathematics Faculty Articles. 124.