摘要
实对称张量的正定性在自动控制系统稳定性、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.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-张量新的判别条件.作为应用,给出了偶数阶实对称张量,即偶次齐次多项式正定性的新实用判定方法.相应数值算例表明了结果的有效性.
The positive definiteness of real symmetric tensors plays an important role in the stability study of automatic control systems, polynomial optimization problems, medical image de-noising problems, etc. 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 of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.
出处
《数学的实践与认识》
北大核心
2016年第10期266-273,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(11501141
11361074)
贵州省科学技术基金([2015]2073)
贵州省科技厅联合基金([2015]7206)
贵州省教育厅自然科学基金([2015]420)
贵州民族大学引进人才科研基金(15XRY004)
关键词
实对称张量
H-张量
不可约
正定性
real symmetric tensors
H-tensors
irreducible
positive definiteness
