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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

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.

Two new eigenvalue localization sets for tensors and theirs applications

88%

Zhao J., Sang C.

Open Mathematics

2017

tom 15

nr 1

1267-1276

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.

Ograniczanie wyników

2 Open Mathematics

2 Sang C.

2 Zhao J.

2 2017

Wyniki wyszukiwania

New bounds for the minimum eigenvalue of 𝓜-tensors

Two new eigenvalue localization sets for tensors and theirs applications