The Schur complements of generalized doubly diagonally dominant matrices. (English) Zbl 1051.15016

It is known that the Schur complements of diagonally dominant matrices are diagonally dominant, and that the same is true for doubly diagonally dominant matrices. In this paper, the authors extend these results to the generalized doubly diagonally dominant matrices (a proper subset of H-matrices); that is, they show that the Schur complement of a generalized doubly diagonally dominant matrix is a generalized doubly diagonally dominant matrix.


15B48 Positive matrices and their generalizations; cones of matrices
65F10 Iterative numerical methods for linear systems
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