The Schur complements of generalized doubly diagonally dominant matrices

By Jianzhou Liu, Yunqing Huang, Fuzhen Zhang. 2004

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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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/db34e85b84746e661251d1303c98a5481c514fe8