The Schur complements of generalized doubly diagonally dominant matrices

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.