On block diagonal-Schur complements of the block strictly doubly diagonally dominant matrices.

As is well known, the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant. In this paper, we verify the block diagonal-Schur complements of I-block strictly doubly diagonally dominant matrices are I-block strictly doubly diagonally dominant matrices, the same is true for II-block strictly doubly diagonally dominant matrices. The theoretical analysis is supported by numerical experiments. [ABSTRACT FROM AUTHOR]