Most Tensor Problems Are NP-Hard

@article{Hillar2009MostTP,
  title={Most Tensor Problems Are NP-Hard},
  author={Christopher J. Hillar and Lek-Heng Lim},
  journal={J. ACM},
  year={2009},
  volume={60},
  pages={45:1-45:39}
}
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or the spectral norm; and determining the rank or best rank-1 approximation of a 3-tensor. Furthermore, we show that restricting these… CONTINUE READING

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