New criteria-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 identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can t...

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Autores principales:	Sun Deshu, Bai Dongjian
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	positive definiteness homogeneous multivariate form ℋ-tensors generalized diagonal dominance iterative scheme 15a69 15a18 65f15 65h17 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2c12dc690d4b4853b36f71cd68e037a7
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spelling	oai:doaj.org-article:2c12dc690d4b4853b36f71cd68e037a72021-12-05T14:10:53ZNew criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms2391-545510.1515/math-2021-0042https://doaj.org/article/2c12dc690d4b4853b36f71cd68e037a72021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0042https://doaj.org/toc/2391-5455Positive definite polynomials are important in the field of optimization. ℋ-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can terminate within finite iterative steps. Some numerical examples are provided to illustrate the efficiency and validity of methods.Sun DeshuBai DongjianDe Gruyterarticlepositive definitenesshomogeneous multivariate formℋ-tensorsgeneralized diagonal dominanceiterative scheme15a6915a1865f1565h17MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 551-561 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	positive definiteness homogeneous multivariate form ℋ-tensors generalized diagonal dominance iterative scheme 15a69 15a18 65f15 65h17 Mathematics QA1-939
spellingShingle	positive definiteness homogeneous multivariate form ℋ-tensors generalized diagonal dominance iterative scheme 15a69 15a18 65f15 65h17 Mathematics QA1-939 Sun Deshu Bai Dongjian New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
description	Positive definite polynomials are important in the field of optimization. ℋ-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can terminate within finite iterative steps. Some numerical examples are provided to illustrate the efficiency and validity of methods.
format	article
author	Sun Deshu Bai Dongjian
author_facet	Sun Deshu Bai Dongjian
author_sort	Sun Deshu
title	New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_short	New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_full	New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_fullStr	New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_full_unstemmed	New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
title_sort	new criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/2c12dc690d4b4853b36f71cd68e037a7
work_keys_str_mv	AT sundeshu newcriteriabasedhtensorsforidentifyingthepositivedefinitenessofmultivariatehomogeneousforms AT baidongjian newcriteriabasedhtensorsforidentifyingthepositivedefinitenessofmultivariatehomogeneousforms
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New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms

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