New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms

New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms

Positive definite polynomials are important in the field of optimization. H-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose some new criterion for identifying H-tensor. As applications, we give new cond...

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Main Authors: Dongjian Bai, Feng Wang
Format: Article
Language:English
Published: AIMS Press 2021-07-01
Series:AIMS Mathematics
Subjects:
homogeneous multivariate form
positive definiteness
h-tensors
irreducible
non-zero element chain
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2021595?viewType=HTML
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spelling doaj-8eb3b969c9b14101baab36ad90e37ab42021-07-27T01:48:15ZengAIMS PressAIMS Mathematics2473-69882021-07-0169102811029510.3934/math.2021595New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous formsDongjian Bai0Feng Wang1College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025, ChinaCollege of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025, ChinaPositive definite polynomials are important in the field of optimization. H-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose some new criterion for identifying H-tensor. As applications, we give new conditions for identifying positive definiteness of the even-order homogeneous multivariate form. At last, some numerical examples are provided to illustrate the efficiency and validity of new methods.https://www.aimspress.com/article/doi/10.3934/math.2021595?viewType=HTMLhomogeneous multivariate formpositive definitenessh-tensorsirreduciblenon-zero element chain
collection DOAJ
language English
format Article
sources DOAJ
author Dongjian Bai
Feng Wang
spellingShingle Dongjian Bai
Feng Wang
New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
AIMS Mathematics
homogeneous multivariate form
positive definiteness
h-tensors
irreducible
non-zero element chain
author_facet Dongjian Bai
Feng Wang
author_sort Dongjian Bai
title New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_short New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_full New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_fullStr New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_full_unstemmed New methods based H-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_sort new methods based h-tensors for identifying the positive definiteness of multivariate homogeneous forms
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2021-07-01
description Positive definite polynomials are important in the field of optimization. H-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose some new criterion for identifying H-tensor. As applications, we give new conditions for identifying positive definiteness of the even-order homogeneous multivariate form. At last, some numerical examples are provided to illustrate the efficiency and validity of new methods.
topic homogeneous multivariate form
positive definiteness
h-tensors
irreducible
non-zero element chain
url https://www.aimspress.com/article/doi/10.3934/math.2021595?viewType=HTML
work_keys_str_mv AT dongjianbai newmethodsbasedhtensorsforidentifyingthepositivedefinitenessofmultivariatehomogeneousforms
AT fengwang newmethodsbasedhtensorsforidentifyingthepositivedefinitenessofmultivariatehomogeneousforms
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