An Improved Iterative Algorithm for Identifying Strong H-Tensors

doi:10.1007/s42967-023-00362-x

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (4): 1598-1614.doi: 10.1007/s42967-023-00362-x

• ORIGINAL PAPERS • 上一篇

An Improved Iterative Algorithm for Identifying Strong H-Tensors

Wenbin Gong, Yan Li, Yaqiang Wang

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, Shaanxi, China

收稿日期:2023-07-08 修回日期:2023-11-02 接受日期:2023-12-03 出版日期:2024-04-02 发布日期:2024-04-02
通讯作者: Yaqiang Wang,E-mail:yaqiangwang1004@163.com E-mail:yaqiangwang1004@163.com
作者简介:Wenbin Gong, E-mail:wenbin0302@163.com;Yan Li, E-mail:yanli9812@163.com
基金资助:
The authors are grateful to the referee for carefully reading of the paper and valuable suggestions and comments.

An Improved Iterative Algorithm for Identifying Strong H-Tensors

Wenbin Gong, Yan Li, Yaqiang Wang

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, Shaanxi, China

Received:2023-07-08 Revised:2023-11-02 Accepted:2023-12-03 Online:2024-04-02 Published:2024-04-02
Supported by:
The authors are grateful to the referee for carefully reading of the paper and valuable suggestions and comments.

摘要/Abstract

摘要： Strong H-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor. In this paper, first, an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor, and the validity of the iterative algorithm is proved theoretically. Second, the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor. Finally, numerical examples are presented to illustrate the advantages of the proposed algorithm.

关键词: Strong H-tensors, Iterative algorithm, Positive diagonal matrix, Symmetric tensors

Abstract: Strong H-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor. In this paper, first, an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor, and the validity of the iterative algorithm is proved theoretically. Second, the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor. Finally, numerical examples are presented to illustrate the advantages of the proposed algorithm.

Key words: Strong H-tensors, Iterative algorithm, Positive diagonal matrix, Symmetric tensors

中图分类号:

Wenbin Gong, Yan Li, Yaqiang Wang. An Improved Iterative Algorithm for Identifying Strong H-Tensors[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1598-1614.

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An Improved Iterative Algorithm for Identifying Strong H-Tensors

An Improved Iterative Algorithm for Identifying Strong H-Tensors

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