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An adaptive gradient method for computing generalized tensor eigenpairs

Author

Listed:
  • Gaohang Yu

    (Gannan Normal University)

  • Zefeng Yu

    (Gannan Normal University)

  • Yi Xu

    (Southeast University)

  • Yisheng Song

    (Henan Normal University)

  • Yi Zhou

    (Sun Yat-Sen University)

Abstract

High order tensor arises more and more often in signal processing, data analysis, higher-order statistics, as well as imaging sciences. In this paper, an adaptive gradient (AG) method is presented for generalized tensor eigenpairs. Global convergence and linear convergence rate are established under some suitable conditions. Numerical results are reported to illustrate the efficiency of the proposed method. Comparing with the GEAP method, an adaptive shifted power method proposed by Kolda and Mayo (SIAM J Matrix Anal Appl 35:1563–1581, 2014) the AG method is much faster and could reach the largest eigenpair with a higher probability.

Suggested Citation

  • Gaohang Yu & Zefeng Yu & Yi Xu & Yisheng Song & Yi Zhou, 2016. "An adaptive gradient method for computing generalized tensor eigenpairs," Computational Optimization and Applications, Springer, vol. 65(3), pages 781-797, December.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9846-9
    DOI: 10.1007/s10589-016-9846-9
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    References listed on IDEAS

    as
    1. Qin Ni & Liqun Qi, 2015. "A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map," Journal of Global Optimization, Springer, vol. 61(4), pages 627-641, April.
    2. Shenglong Hu & Guoyin Li & Liqun Qi & Yisheng Song, 2013. "Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 717-738, September.
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    Cited by:

    1. Na Zhao & Qingzhi Yang & Yajun Liu, 2017. "Computing the generalized eigenvalues of weakly symmetric tensors," Computational Optimization and Applications, Springer, vol. 66(2), pages 285-307, March.
    2. Mengshi Zhang & Guyan Ni & Guofeng Zhang, 2020. "Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement," Computational Optimization and Applications, Springer, vol. 75(3), pages 779-798, April.
    3. Mengshi Zhang & Xinzhen Zhang & Guyan Ni, 2019. "Calculating Entanglement Eigenvalues for Nonsymmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 787-802, March.

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