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引用次数: 0
摘要
$ \mathcal{H} $-张量在确定偶阶实对称张量的正定性方面起着关键作用。由于很难判断给定张量是否为$ \mathcal{H} $-张量,因此给出了一些准则,并且它们的判断范围受到限制。本文给出了从一个递增的常数$ k $缩放给定张量的元素可以扩大判断范围的一些新准则。此外,作为这些新准则的应用,给出了判定偶阶实对称张量正确定性的几个充分条件。此外,还给出了一些数值算例来说明这些新结果。
Some new criteria for judging $ \mathcal{H} $-tensors and their applications
$ \mathcal{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 $ \mathcal{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.
期刊介绍:
AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.