scholarly journals Some improvements on the Ky Fan theorem for tensors

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Mohsen Tourang ◽  
Mostafa Zangiabadi
Keyword(s):  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Fan Theorem ◽  
Linear Multilinear Algebra ◽  
Numer Math ◽  
Ky Fan ◽  
Localization Sets ◽  
Ky Fan Theorem ◽  
Perron Vector

AbstractThe improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315–335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817–1834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.

scholarly journals Improved Brauer-type eigenvalue localization sets for tensors with their applications

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4607-4625
Author(s):  
Zhengge Huang ◽  
Jingjing Cui
Keyword(s):  
Linear Algebra ◽  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
New Criteria ◽  
Localization Sets ◽  
Better Than

In this paper, by excluding some sets from the Brauer-type eigenvalue inclusion sets for tensors developed by Bu et al. (Linear Algebra Appl. 512 (2017) 234-248) and Li et al. (Linear and Multilinear Algebra 64 (2016) 727-736), some improved Brauer-type eigenvalue localization sets for tensors are given, which are proved to be much tighter than those put forward by Bu et al. and Li et al. As applications, some new criteria for identifying the nonsingularity of tensors are developed, which are better than some previous results. This fact is illustrated by some numerical examples.

scholarly journals An improvement of Ky Fan theorem for matrix eigenvalues

2005 ◽  
Vol 49 (5-6) ◽  
pp. 789-803 ◽  
Author(s):  
Hou-Biao Li ◽  
Ting-Zhu Huang
Keyword(s):  
Fan Theorem ◽  
Matrix Eigenvalues ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Ky Fan theorem applied to Randić energy

2014 ◽  
Vol 459 ◽  
pp. 23-42 ◽  
Author(s):  
Ivan Gutman ◽  
Enide A. Martins ◽  
María Robbiano ◽  
Bernardo San Martín
Keyword(s):  
Fan Theorem ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Wielandt and Ky-Fan theorem for matrix pairs

2003 ◽  
Vol 369 ◽  
pp. 77-93 ◽  
Author(s):  
Ivica Nakić ◽  
Krešimir Veselić
Keyword(s):  
Fan Theorem ◽  
Ky Fan ◽  
Ky Fan Theorem

scholarly journals Inequalities for certain Classes of Convex Functions

1959 ◽  
Vol 11 (4) ◽  
pp. 231-235 ◽  
Author(s):  
L. Mirsky
Keyword(s):  
Simple Proof ◽  
Convex Functions ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Fan Theorem ◽  
Special Cases ◽  
Gauge Functions ◽  
Ky Fan ◽  
Ky Fan Theorem ◽  
Symmetric Gauge

Making use of properties of doubly-stochastic matrices, I recently gave a simple proof (4) of a theorem of Ky Fan (Theorem 2b below) on symmetric gauge functions. I now propose to show that the same idea can be employed to derive a whole series of results on convex functions ; in particular, certain well-known inequalities of Hardy-Littlewood-Pólya and of Pólya will emerge as specìal cases.

scholarly journals Two new eigenvalue localization sets for tensors and theirs applications

2017 ◽  
Vol 15 (1) ◽  
pp. 1267-1276 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Linear Algebra ◽  
Symmetric Tensor ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Even Order ◽  
Weakly Symmetric ◽  
Localization Set ◽  
Theoretical Results ◽  
Localization Sets

Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1), 187-198). As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

scholarly journals New Refinement of the Operator Kantorovich Inequality

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 139
Author(s):  
Hamid Moradi ◽  
Shigeru Furuichi ◽  
Zahra Heydarbeygi
Keyword(s):  
Multilinear Algebra ◽  
Kantorovich Inequality ◽  
Linear Multilinear Algebra

We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multilinear Algebra, doi:10.1080/03081087.2018.1441799].

Sign in / Sign up

Export Citation Format

Share Document