摘要👨🏼‍🔧：The Schur complement of matrix is an important tool for dealing with reducing order problem. In this talk, we firstly introduce the relations between the original matrices and the Schur complements of its submatrices of several special matrices and show the eigenvalue distribution of H matrix. Secondly, we discuss the dominant degree of the Schur complements of diagonally dominant matrices. Further, applying dominant degree, we present the corresponding disc theorems on the Schur complements ofdiagonally dominant matrices. Thirdly, we study the dominant degree and disc theorems of the Schur complements of block diagonally dominant matrices. Finally, 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 the numerical example illustrates that the iteration can compute out the results faster.