Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

@inproceedings{Carrington2021ComputingVE,
  title={Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank},
  author={Tucker Carrington and Sangeeth Kallullathil},
  year={2021}
}
Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about 5 atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use CP format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block… 

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On the Convergence of Alternating Least Squares Optimisation in Tensor Format Representations
TLDR
The convergence of the alternating least squares algorithm is considered for arbitrary tensor format representations and based on the multiliearity of the Tensor format.