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Subtracting a best rank-1 approximation from p × p × 2(p≥2) tensors

Authors

  • Xu Kong,

    1. Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, People's Republic of China
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  • Yao-Lin Jiang

    Corresponding author
    1. Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, People's Republic of China
    • Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, People's Republic of China
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SUMMARY

We introduce one special form of the ptimesp × 2 (p≥2) tensors by multilinear orthonormal transformations, and present some interesting properties of the special form. Through discussing on the special form, we provide a solution to one conjecture proposed by Stegeman and Comon in a conference paper (Proceedings of the EUSIPCO 2009 Conference, Glasgow, Scotland, 2009), and reveal an important conclusion about subtracting a best rank-1 approximations from p × p × 2 tensors of the special form. All of these confirm that consecutively subtracting the best rank-1 approximations may not lead to a best low rank approximation of a tensor. Numerical examples show the correctness of our theory. Copyright © 2011 John Wiley & Sons, Ltd.

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