The Schur complements of γ-diagonally and product γ-diagonally dominant matrix and their disc separation

In this paper, we obtain some estimates for the γ-diagonally and product γ-diagonally dominant degree of the Schur complement of matrices. As application we present some bounds for the eigenvalues of Schur complement by the entries of the original matrix. Based on these results, we give a kind of iteration called the Schur-based iteration, which can solve large scale linear systems though reducing the order by the Schur complement and can compute out the results faster.