The new improved estimates of the dominant degree and disc theorem for the Schur complement of matrices
Jingjing Cui, Guohua Peng, Quan Lu, Zhengge Huang · Linear and Multilinear Algebra · 2016
The theory of Schur complement is very important in many fields such as control theory and computational mathematics. In this paper, by applying the properties of the Schur complement and some inequality techniques, some new estimates of the diagonally, -diagonally and product -diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. Further, as an application of these derived results, we present some distributions for the eigenvalues of the Schur complements. Finally, the numerical example is given to show the advantages of our derived results.