On Schur complements of Dashnic–Zusmanovich type matrices

Abstract

It is shown in this paper that the Schur complements and the diagonal-Schur complements of DZ-type matrices are DZ-type matrices under some conditions. A numerical example for solving the linear equations with the coefficient matrix being a DZ-type matrix is given to show that the Schur-based Gauss–Seidel iteration method and the Schur-based conjugate gradient method can compute out the solution faster.