scholarly journals Exclusion sets in Dashnic–Zusmanovich localization sets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jianxing Zhao ◽  
Lili She
Keyword(s):  
Localization Sets

scholarly journals Some new inclusion sets for eigenvalues of tensors with application

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3899-3916
Author(s):  
Zhengge Huang ◽  
Ligong Wang ◽  
Zhong Xu ◽  
Jingjing Cui
Keyword(s):  
Symmetric Tensors ◽  
Eigenvalue Localization ◽  
Even Order ◽  
Localization Sets ◽  
Eigenvalues Of Tensors

In this paper, we are concerned with the eigenvalue inclusion sets for tensors. Some new S-type eigenvalue localization sets for tensors are employed by dividing N = {1,2,..., n} into disjoint subsets S and its complement. Our new sets, are proved to be tighter than that newly derived by Huang et al. (J. Inequal. Appl. 2016 (2016) 254). As applications, we can apply the proposed sets for determining the positive (semi-)definiteness of even-order symmetric tensors. Some examples are given to show the sharpness of our new sets in contrast with the known ones, and verify the effectiveness of those in identifying the positive (semi-)definiteness of tensors.

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.

Exclusion sets in the S-type eigenvalue localization sets for tensors

2019 ◽  
Vol 17 (1) ◽  
pp. 1136-1146 ◽  
Author(s):  
Yuan Zhang ◽  
Ying Zhang ◽  
Gang Wang
Keyword(s):  
Numerical Results ◽  
Index Set ◽  
Eigenvalue Localization ◽  
Localization Sets

Abstract In this paper, we break the index set N into disjoint subsets S and its complement, and propose two S-type exclusion sets that all the eigenvalues do not belong to them. Furthermore, we establish new S-type eigenvalue inclusion sets, which can reduce computations and obtain more accurate numerical results. At the same time, we give two criteria for identifying nonsingular tensors. Finally, new S-type eigenvalue inclusion sets are shown to be sharper than existing results via two examples.

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.

Sign in / Sign up

Export Citation Format

Share Document