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1
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Bounds for the Z-eigenpair of general nonnegative tensors

100%
Liu Q., Li Y.
Open Mathematics
|
2016
|
tom 14
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nr 1
181-194
EN
In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.
2
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New iterative codes for𝓗-tensors and an application

100%
Wang F., Sun D.
Open Mathematics
|
2016
|
tom 14
|
nr 1
212-220
EN
New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.
3
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AnS-type upper bound for the largest singular value of nonnegative rectangular tensors

100%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
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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.
4
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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.
5
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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.
6
Content available remote

Bound for the largest singular value of nonnegative rectangular tensors

84%
He J., Liu Y.-M., Ke H., Tian J.-K., Li X.
Open Mathematics
|
2016
|
tom 14
|
nr 1
761-766
EN
In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math. China, 2011, 6, 363-378.
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