New methods based $ \mathcal{H} $-tensors for identifying the positive definiteness of multivariate homogeneous forms

Dongjian Bai; Feng Wang; Dongjian Bai; Feng Wang

doi:10.3934/math.2021595

AIMS Mathematics

2021, Volume 6, Issue 9: 10281-10295. doi: 10.3934/math.2021595

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Research article

New methods based $ \mathcal{H} $-tensors for identifying the positive definiteness of multivariate homogeneous forms

Dongjian Bai ,
Feng Wang ^,

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

Received: 27 April 2021 Accepted: 05 July 2021 Published: 13 July 2021
MSC : 15A18, 15A69, 65F15, 65H17

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.
- homogeneous multivariate form,
- positive definiteness,
- $ \mathcal{H} $-tensors,
- irreducible,
- non-zero element chain
Citation: Dongjian Bai, Feng Wang. New methods based $ \mathcal{H} $-tensors for identifying the positive definiteness of multivariate homogeneous forms[J]. AIMS Mathematics, 2021, 6(9): 10281-10295. doi: 10.3934/math.2021595

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Abstract

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.

References

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