Criterions for the positive definiteness of real supersymmetric tensors

• Autores: Chaoqian Li, Feng Wang, Jianxing Zhao, Yan Zhu, Yaotang Li
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 1-14
• Idioma: inglés
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• Resumen

  • The positive definiteness of an even-degree homogeneous polynomial form f (x) 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 f (x) is equivalent to that of an even-order supersymmetric tensor which defines f (x). 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 evenorder real supersymmetric tensor is obtained. Numerical examples are given to verify the corresponding results.