The Doubly Diagonally Dominant Degree of the Schur Complement of Strictly Doubly Diagonally Dominant Matrices and Its Applications

2020 ◽  
Author(s):  
Jiangliu Gu ◽  
Shouwei Zhou ◽  
Jianxing Zhao ◽  
Jiafeng Zhang
Keyword(s):  
Schur Complement ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant

The Schur Complement on Weak Block Diagonally Dominant Matrices and Weak Block H-Matrices

2011 ◽  
Vol 148-149 ◽  
pp. 1523-1526
Author(s):  
Shi Hong Liu ◽  
Hong Su ◽  
Zhuo Hong Huang
Keyword(s):  
Schur Complement ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant

In this paper, we prove that the Schur complement of Weak block diagonally dominant matrices and weak block H-matrices are Weak block diagonally dominant matrices and weak block H-matrices, respectively.

scholarly journals The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Feng Wang ◽  
Deshu Sun
Keyword(s):  
Control Theory ◽  
Linear Algebra ◽  
Matrix Theory ◽  
Schur Complement ◽  
Numerical Example ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
And Control

AbstractThe theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. 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.

scholarly journals On Schur complement of block diagonally dominant matrices

2006 ◽  
Vol 414 (2-3) ◽  
pp. 533-546 ◽  
Author(s):  
Cheng-yi Zhang ◽  
Yao-tang Li ◽  
Feng Chen
Keyword(s):  
Schur Complement ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant
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