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Randomized algorithms for the computation of multilinear rank- $$(\mu _1,\mu _2,\mu _3)$$ ( μ 1 , μ 2 , μ 3 ) approximations

Author

Listed:
  • Maolin Che

    (Southwestern University of Finance and Economics)

  • Yimin Wei

    (Fudan University)

  • Yanwei Xu

    (Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co., Ltd.)

Abstract

We present some randomized algorithms for computing multilinear rank- $$(\mu _1,\mu _2,\mu _3)$$ ( μ 1 , μ 2 , μ 3 ) approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples.

Suggested Citation

  • Maolin Che & Yimin Wei & Yanwei Xu, 2023. "Randomized algorithms for the computation of multilinear rank- $$(\mu _1,\mu _2,\mu _3)$$ ( μ 1 , μ 2 , μ 3 ) approximations," Journal of Global Optimization, Springer, vol. 87(2), pages 373-403, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01182-8
    DOI: 10.1007/s10898-022-01182-8
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