scholarly journals Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse

2011 ◽  
Vol 22 ◽  
Author(s):  
Yaotang Li ◽  
Xin Liu ◽  
Xiaoying Yang ◽  
Chaoqian Li
Keyword(s):  
Lower Bounds ◽  
Hadamard Product ◽  
Minimum Eigenvalue

scholarly journals Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse

2007 ◽  
Vol 420 (1) ◽  
pp. 235-247 ◽  
Author(s):  
Hou-Biao Li ◽  
Ting-Zhu Huang ◽  
Shu-Qian Shen ◽  
Hong Li
Keyword(s):  
Lower Bounds ◽  
Hadamard Product ◽  
Minimum Eigenvalue

scholarly journals Some new bounds of the minimum eigenvalue for the Hadamard product of an M-matrix and an inverse M-matrix

2016 ◽  
Vol 14 (1) ◽  
pp. 81-88
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Lower Bounds ◽  
Hadamard Product ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
True Value ◽  
Convergent Sequences

AbstractSome convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.

On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mustafa Özel ◽  
Dilek Varol
Keyword(s):  
Lower Bounds ◽  
Hadamard Product ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Better Than

AbstractRecently, some authors have established a number of inequalities involving the minimum eigenvalue for the Hadamard product of M-matrices. In this paper, we improve these results and give some new lower bounds on the minimum eigenvalue for the Hadamard product of an M-matrix A and its inverse {A^{-1}}. Finally, it is shown by the numerical examples that our bounds are also better than some previous results.

scholarly journals Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 147
Author(s):  
Qianping Guo ◽  
Jinsong Leng ◽  
Houbiao Li ◽  
Carlo Cattani
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Upper Bound ◽  
Hadamard Product ◽  
Simple Type ◽  
Nonnegative Matrices ◽  
Minimum Eigenvalue ◽  
Numerical Examples ◽  
Product Of Matrices

In this paper, an upper bound on the spectral radius ρ ( A ∘ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ★ D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.

scholarly journals New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse

2009 ◽  
Vol 430 (4) ◽  
pp. 1423-1431 ◽  
Author(s):  
Yao-Tang Li ◽  
Fu-Bin Chen ◽  
De-Feng Wang
Keyword(s):  
Lower Bounds ◽  
Hadamard Product

scholarly journals Inequalities for the Minimum Eigenvalue of Doubly Strictly Diagonally DominantM-Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ming Xu ◽  
Suhua Li ◽  
Chaoqian Li
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Matrix Inequalities ◽  
Minimum Eigenvalue ◽  
Minimal Eigenvalue ◽  
Diagonally Dominant ◽  
Linear Differential ◽  
New Inequalities

LetAbe a doubly strictly diagonally dominantM-matrix. Inequalities on upper and lower bounds for the entries of the inverse ofAare given. And some new inequalities on the lower bound for the minimal eigenvalue ofAand the corresponding eigenvector are presented to establish an upper bound for theL1-norm of the solutionx(t)for the linear differential systemdx/dt=-Ax(t),x(0)=x0>0.

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