An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor and its an application

Tinglan Yao; Tinglan Yao

doi:10.3934/math.2022058

AIMS Mathematics

2022, Volume 7, Issue 1: 967-985. doi: 10.3934/math.2022058

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Research article

An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor and its an application

Tinglan Yao ^,

College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou, 550025, China

Received: 17 August 2021 Accepted: 14 October 2021 Published: 19 October 2021
MSC : 15A18, 15A42, 15A69

An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.
- sixth-order tensors,
- $ Z $-eigenvalues,
- inclusion intervals,
- positive definiteness
Citation: Tinglan Yao. An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor and its an application[J]. AIMS Mathematics, 2022, 7(1): 967-985. doi: 10.3934/math.2022058

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Abstract

An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.

References

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