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The point-wise convergence of shifted symmetric higher order power method

  • * Corresponding author: Qingzhi Yang

    * Corresponding author: Qingzhi Yang

The second author is supported by Natural Science Foundation of Xinjiang (Grant No. 2017D01A14)

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  • Shifted symmetric higher-order power method (SS-HOPM) is an effective method of computing tensor eigenpairs. However the point-wise convergence of SS-HOPM has not been proven yet. In this paper, we provide a solid proof of the point-wise convergence of SS-HOPM via Łojasiewicz inequality. In particular, we establish a mapping from the sequence generated by the algorithm to a specially defined sequence. Using Łojasiewicz inequality, we prove the convergence of the new sequence, then the original sequence is convergent based on the relation of two sequences.

    Mathematics Subject Classification: Primary: 15A18, 90C26; Secondary: 15A69.


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  • Figure 1.  Trajectories of sequences $ \{x_k\} $, $ \{y_k\} $ generated by SS-HOPM

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