Singular values of nonnegative rectangular tensors |
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Authors: | Yuning Yang Qingzhi Yang |
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Institution: | School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
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Abstract: | 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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Keywords: | Nonnegative rectangular tensor Perron-Frobenius Theorem singular value algorithm |
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