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Keywords = ℋ+-tensor

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17 pages, 309 KB  
Article
New Criterions-Based H-Tensors for Testing the Positive Definiteness of Multivariate Homogeneous Forms
by Dongjian Bai and Feng Wang
Mathematics 2022, 10(14), 2416; https://doi.org/10.3390/math10142416 - 11 Jul 2022
Cited by 1 | Viewed by 1412
Abstract
Positive definite homogeneous multivariate forms play an important role in polynomial problems and medical imaging, and the definiteness of forms can be tested using structured tensors. In this paper, we state the equivalence between the positive definite multivariate forms and the corresponding tensors, [...] Read more.
Positive definite homogeneous multivariate forms play an important role in polynomial problems and medical imaging, and the definiteness of forms can be tested using structured tensors. In this paper, we state the equivalence between the positive definite multivariate forms and the corresponding tensors, and explain the connection between the positive definite tensors with H-tensors. Then, based on the notion of diagonally dominant tensors, some criteria for H-tensors are presented. Meanwhile, with these links, we provide an iterative algorithm to test the positive definiteness of multivariate homogeneous forms and prove its validity theoretically. The advantages of the obtained results are illustrated by some numerical examples. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
9 pages, 329 KB  
Article
A Tensor Splitting AOR Iterative Method for Solving a Tensor Absolute Value Equation
by Yuhan Chen and Chenliang Li
Mathematics 2022, 10(7), 1023; https://doi.org/10.3390/math10071023 - 23 Mar 2022
Cited by 6 | Viewed by 2248
Abstract
In this paper, a tensor splitting AOR iterative method for solving the H+-tensor absolute value equation is presented. Some sufficient conditions for the existence of the solution to the tensor absolute value equation are given. Under suitable conditions, the new method [...] Read more.
In this paper, a tensor splitting AOR iterative method for solving the H+-tensor absolute value equation is presented. Some sufficient conditions for the existence of the solution to the tensor absolute value equation are given. Under suitable conditions, the new method is proved to be convergent. Finally, some numerical examples demonstrate that our new method is effective. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing II)
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13 pages, 771 KB  
Article
Practical Criteria for H-Tensors and Their Application
by Min Li, Haifeng Sang, Panpan Liu and Guorui Huang
Symmetry 2022, 14(1), 155; https://doi.org/10.3390/sym14010155 - 13 Jan 2022
Cited by 2 | Viewed by 1842
Abstract
Identifying the positive definiteness of even-order real symmetric tensors is an important component in tensor analysis. H-tensors have been utilized in identifying the positive definiteness of this kind of tensor. Some new practical criteria for identifying H-tensors are given in the [...] Read more.
Identifying the positive definiteness of even-order real symmetric tensors is an important component in tensor analysis. H-tensors have been utilized in identifying the positive definiteness of this kind of tensor. Some new practical criteria for identifying H-tensors are given in the literature. As an application, several sufficient conditions of the positive definiteness for an even-order real symmetric tensor were obtained. Numerical examples are given to illustrate the effectiveness of the proposed method. Full article
(This article belongs to the Topic Applied Metaheuristic Computing)
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