Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds

Authors

Jianzhou Liu, Xiangtan University
Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

12-1-2005

Publication Title

SIAM Journal on Matrix Analysis and Applications

Keywords

Brauer theorem, Comparison matrix, Diagonally dominant matrix, Doubly diagonally dominant matrix, Gersgorin theorem, H-matrix, M-matrix, Schur complement, Separation

ISSN

0895-4798

Volume

27

Issue/No.

3

First Page

665

Last Page

674

Abstract

We consider the Gersgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of diagonally dominant matrices.

Comments

AMS subject classifications. 15A45, 15A48

NSUWorks Citation

Liu, Jianzhou and Zhang, Fuzhen, "Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds" (2005). Mathematics Faculty Articles. 51.
https://nsuworks.nova.edu/math_facarticles/51

DOI

10.1137/040620369