Computation of extreme eigenvalues in higher dimensions using block tensor train format

S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, D. V. Savostyanov

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66 Citations (SciVal)


We consider approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high-dimensional problems. We use the tensor train (TT) format for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. We approximate several low-lying eigenvectors simultaneously in the block version of the TT format. The computation is done by the alternating minimization of the block Rayleigh quotient sequentially for all TT cores. The proposed method combines the advances of the density matrix renormalization group (DMRG) and the variational numerical renormalization group (vNRG) methods. We compare the performance of the proposed method with several versions of the DMRG codes, and show that it may be preferable for systems with large dimension and/or mode size, or when a large number of eigenstates is sought.

Original languageEnglish
Pages (from-to)1207-1216
Number of pages10
JournalComputer Physics Communications
Issue number4
Publication statusPublished - 1 Apr 2014


  • DMRG
  • High-dimensional problems
  • Low-lying eigenstates
  • MPS
  • Tensor train format

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)


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