摘要
H-张量在自动控制系统的稳定性、多项式全局优化、医疗影像降噪等问题中具有重要的应用价值.但在实际中要判定一给定张量为H-张量比较困难.本文通过构造不同的正对角阵和运用不等式的放缩技巧,给出了H-张量一组新的实用判定方法.作为应用,给出了偶数阶实对称张量正定性的新判定条件.相应数值示例说明了结果的有效性.
H-tensors play an important role in the stability study of automatic control systems, polynomial optimization problems, medical image de-noising problems, and so on. But it is not easy to determine whether a given tensor is an H-tensor or not in practice. In this paper, we give some practical criteria for H-tensors by constructing different positive diagonal matrices and applying some techniques of inequalities. As an application, some sufficient conditions for the positive definiteness of an even-order real symmetric tensor are given. Advantages of obtained results are illustrated by numerical examples.
出处
《工程数学学报》
CSCD
北大核心
2016年第3期287-297,共11页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11361074
11501141)
贵州省科学技术基金([2015]2073)
贵州省教育厅自然科学基金([2015]420)
贵州民族大学科研基金(15XRY004)~~
关键词
H-张量
实对称张量
正定性
不可约
非零元素链
H-tensors
real symmetric tensors
positive definiteness
irreducible
nonzero elements chain
