H-张量的新判定准则及其应用
New Criterions for H-Tensors and Its Applications
DOI: 10.12677/AAM.2022.118604, PDF,    科研立项经费支持
作者: 赵鹏程：贵州民族大学数据科学与信息工程学院，贵州 贵阳
关键词: H-张量；齐次多项式；正定性；不可约；非零元素链；H-Tensors； Homogeneous Multivariate Forms； Positive Definiteness； Irreducible； Nonzero Elements Chain
摘要: H-张量在科学与工程实践等领域中有着重要的应用，但在实际中要判定H-张量是比较困难的。本文通过构造不同的正对角阵，结合不等式的放缩技巧，给出了H-张量比较实用的新判别条件。作为应用，给出了判定偶次齐次多项式正定性的新方法，并给出相应的数值算例，表明了新结论的有效性。
Abstract: H-tensors have important applications in science and engineering, but it is difficult to determine whether a given tensor is an H-tensor or not in practice. In this paper, by constructing different pos-itive diagonal matrices and combining the technique of inequality reduction, new practical condi-tions for H-tensors are given. As applications, new methods for determining the positive definite-ness of even homogeneous polynomials are presented, and the validity of new results is verified by some numerical examples.
文章引用：赵鹏程. H-张量的新判定准则及其应用[J]. 应用数学进展, 2022, 11(8): 5727-5736. https://doi.org/10.12677/AAM.2022.118604

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