Some new criteria for judging H-tensors and their applications

H-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an H-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increas...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 4; pp. 7606 - 7617
Main Authors Wenbin Gong, Yaqiang Wang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
h-tensor
judging range
positive definiteness
positive diagonal matrix
symmetric tensor
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Summary:H-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an H-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increasing constant k to scale the elements of a given tensor can expand the range of judgment, are obtained. Moreover, as an application of those new criteria, some sufficient conditions for judging positive definiteness of even-order real symmetric tensors are proposed. In addition, some numerical examples are presented to illustrate those new results.
ISSN:2473-6988
DOI:10.3934/math.2023381