TITLE:
The Estimates of Diagonally Dominant Degree and Eigenvalue Inclusion Regions for the Schur Complement of Matrices
AUTHORS:
Dongjie Gao
KEYWORDS:
Schur Complement, Gerschgorin Theorem, Diagonally Dominant Degree, Eigenvalue
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.10,
August
26,
2015
ABSTRACT: The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.