An -tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms

详细信息    查看全文

• 作者：Kaili Zhang ^{zh_kaili@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yiju Wang ; ^{wang-yiju@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A18 ; 15A69 ; 65F15 ; 65F10
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：1-10
• 全文大小：405 K

文摘

Identifying the positive definiteness of an even-order homogeneous multivariate form is an important task due to its wide applications in such as medical imaging and the stability analysis of nonlinear autonomous systems via Lyapunov’s direct method in automatic control and multivariate network realizability analysis. In this paper, based on the equivalence of the positive definiteness of the form to that of the underlying tensor, and the links between the positive definiteness of a tensor with strong H$H$-tensor, we propose an H$H$-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms. The validity of the iterative scheme is guaranteed theoretically and the given numerical experiments show the efficiency of the scheme.