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  1. 4 Open Mathematics

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  1. 4 Sang C.

  2. 4 Zhao J.

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  1. 2 2017

  2. 2 2016

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Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

100%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
81-88
EN
Some 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.
2
Content available remote

AnS-type upper bound for the largest singular value of nonnegative rectangular tensors

100%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
925-933
EN
An S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.
3
Content available remote

New bounds for the minimum eigenvalue of 𝓜-tensors

100%
Zhao J., Sang C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
296-303
EN
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.
4
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Two new eigenvalue localization sets for tensors and theirs applications

100%
Zhao J., Sang C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1267-1276
EN
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.
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