Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets

Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets

The positive definiteness of even-order weakly symmetric tensors plays important roles in asymptotic stability of time-invariant polynomial systems. In this paper, we establish two Brauer-type <i>Z</i>-eigenvalue inclusion sets with parameters by <i>Z</i>-identity tensors, an...

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Main Authors: Feichao Shen, Ying Zhang, Gang Wang
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Symmetry
Subjects:
<i>Z</i>-eigenvalue inclusion set
positive definiteness
asymptotic stability
weakly symmetric tensor
Online Access:https://www.mdpi.com/2073-8994/13/7/1239
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spelling doaj-5019a459287f407bbe3582dded06b99f2021-07-23T14:09:24ZengMDPI AGSymmetry2073-89942021-07-01131239123910.3390/sym13071239Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion SetsFeichao Shen0Ying Zhang1Gang Wang2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Basic Teaching, Shandong Water Conservancy Vocational College, Rizhao 276826, ChinaSchool of Management Science, Qufu Normal University, Rizhao 276826, ChinaThe positive definiteness of even-order weakly symmetric tensors plays important roles in asymptotic stability of time-invariant polynomial systems. In this paper, we establish two Brauer-type <i>Z</i>-eigenvalue inclusion sets with parameters by <i>Z</i>-identity tensors, and show that these inclusion sets are sharper than existing results. Based on the new <i>Z</i>-eigenvalue inclusion sets, we propose some sufficient conditions for testing the positive definiteness of even-order weakly symmetric tensors, as well as the asymptotic stability of time-invariant polynomial systems. The given numerical experiments are reported to show the efficiency of our results.https://www.mdpi.com/2073-8994/13/7/1239<i>Z</i>-eigenvalue inclusion setpositive definitenessasymptotic stabilityweakly symmetric tensor
collection DOAJ
language English
format Article
sources DOAJ
author Feichao Shen
Ying Zhang
Gang Wang
spellingShingle Feichao Shen
Ying Zhang
Gang Wang
Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
Symmetry
<i>Z</i>-eigenvalue inclusion set
positive definiteness
asymptotic stability
weakly symmetric tensor
author_facet Feichao Shen
Ying Zhang
Gang Wang
author_sort Feichao Shen
title Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
title_short Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
title_full Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
title_fullStr Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
title_full_unstemmed Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via <i>Z</i>-Eigenvalue Inclusion Sets
title_sort identifying the positive definiteness of even-order weakly symmetric tensors via <i>z</i>-eigenvalue inclusion sets
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-07-01
description The positive definiteness of even-order weakly symmetric tensors plays important roles in asymptotic stability of time-invariant polynomial systems. In this paper, we establish two Brauer-type <i>Z</i>-eigenvalue inclusion sets with parameters by <i>Z</i>-identity tensors, and show that these inclusion sets are sharper than existing results. Based on the new <i>Z</i>-eigenvalue inclusion sets, we propose some sufficient conditions for testing the positive definiteness of even-order weakly symmetric tensors, as well as the asymptotic stability of time-invariant polynomial systems. The given numerical experiments are reported to show the efficiency of our results.
topic <i>Z</i>-eigenvalue inclusion set
positive definiteness
asymptotic stability
weakly symmetric tensor
url https://www.mdpi.com/2073-8994/13/7/1239
work_keys_str_mv AT feichaoshen identifyingthepositivedefinitenessofevenorderweaklysymmetrictensorsviaizieigenvalueinclusionsets
AT yingzhang identifyingthepositivedefinitenessofevenorderweaklysymmetrictensorsviaizieigenvalueinclusionsets
AT gangwang identifyingthepositivedefinitenessofevenorderweaklysymmetrictensorsviaizieigenvalueinclusionsets
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