The Schur complement of SDD ${}_1$ matrices and its applications

The Schur complements of H-matrices have a wide range of practical applications. This paper explores the diagonally dominant degrees of the Schur complements of SDD ${}_1$ matrices and its applications. it concludes that the Schur complements can be also SDD ${}_1$ matrices under certain conditions. Moreover, the upper and lower bounds for the determinants of SDD ${}_1$ matrices are presented, and large-scale linear equations with the coefficient matrix being an SDD ${}_1$ matrix are solved by Schur-based methods. The numerical results are reported.