Open AccessNew methods based $ \mathcal{H} $-tensors for identifying the positive definiteness of multivariate homogeneous forms
Author(s) -
Dongjian Bai,
Feng Wang
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021595
Subject(s) - positive definiteness , definiteness , homogeneous , multivariate statistics , positive definite matrix , mathematics , tensor (intrinsic definition) , order (exchange) , homogeneous polynomial , multivariate analysis , field (mathematics) , pure mathematics , combinatorics , mathematical analysis , statistics , physics , linguistics , polynomial , philosophy , quantum mechanics , eigenvalues and eigenvectors , finance , matrix polynomial , economics
Positive definite polynomials are important in the field of optimization. $ \mathcal{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 $ \mathcal{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.