Criterions for the positive definiteness of real supersymmetric tensors
详细信息 查看全文
- 作者：Chaoqian Li ; Feng Wang ; Jianxing Zhao ; Yan Zhu ; Yaotang Li
- 关键词：15A69 ; 12E05 ; 12E10
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2014
- 出版时间：1 January, 2014
- 年：2014
- 卷：255
- 期：Complete
- 页码：1-14
- 全文大小：418 K
文摘
The positive definiteness of an even-degree homogeneous polynomial form plays an important role in the stability study of nonlinear autonomous systems via Lyapunov¡¯s direct method in automatic control, and the positive definiteness of is equivalent to that of an even-order supersymmetric tensor which defines . In this paper, we provide some criterions for identifying the positive definiteness of an even-order real supersymmetric tensor. Moreover, an iterative algorithm for identifying the positive definiteness of an even-order real supersymmetric tensor is obtained. Numerical examples are given to verify the corresponding results.