H-张量的新判定准则及其应用  

New Criterions for H-Tensors and Its Applications

作　　者：赵鹏程 

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州 贵阳

出　　处：《应用数学进展》2022年第8期5727-5736,共10页Advances in Applied Mathematics

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。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.

关 键 词：H-张量 齐次多项式 正定性 不可约 非零元素链 

分 类 号：O183.2[理学—数学]