Singular values of nonnegative rectangular tensors

被引：0
作者：
Yuning Yang
Qingzhi Yang
机构：
[1] Nankai University,School of Mathematical Sciences and LPMC
来源：
Frontiers of Mathematics in China | 2011年 / 6卷
关键词：
Nonnegative rectangular tensor; Perron-Frobenius Theorem; singular value; algorithm; 74B99; 15A18; 15A69;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. Some properties concerning the singular values of a real rectangular tensor were discussed by K. C. Chang et al. [J. Math. Anal. Appl., 2010, 370: 284–294]. In this paper, we give some new results on the Perron-Frobenius Theorem for nonnegative rectangular tensors. We show that the weak Perron-Frobenius keeps valid and the largest singular value is really geometrically simple under some conditions. In addition, we establish the convergence of an algorithm proposed by K. C. Chang et al. for finding the largest singular value of nonnegative primitive rectangular tensors.
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页码：363 / 378
页数：15
相关论文
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