%0 Journal Article
%T H-张量的新判定准则及其应用<br>New Criterions for H-Tensors and Its Applications
%A 赵鹏程
%J Advances in Applied Mathematics
%P 5727-5736
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.118604
%X 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。<br />
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.
%K H-张量，齐次多项式，正定性，不可约，非零元素链<br>H-Tensors
%K Homogeneous Multivariate Forms
%K Positive Definiteness
%K Irreducible
%K Nonzero 
Elements Chain
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=54852