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

Sergey Dolgov, Boris Khoromskij, Ivan Oseledets, Dmitry Savostyanov

Research output: Contribution to journalArticle

Abstract

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
Volume185
Issue number4
DOIs
Publication statusPublished - 27 Dec 2013

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Tensors
Eigenvalues and eigenfunctions
Costs

Bibliographical note

© 2013. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

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

Cite this

Dolgov, Sergey ; Khoromskij, Boris ; Oseledets, Ivan ; Savostyanov, Dmitry. / Computation of extreme eigenvalues in higher dimensions using block tensor train format. In: Computer Physics Communications. 2013 ; Vol. 185, No. 4. pp. 1207-1216.
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Computation of extreme eigenvalues in higher dimensions using block tensor train format. / Dolgov, Sergey; Khoromskij, Boris; Oseledets, Ivan; Savostyanov, Dmitry.

In: Computer Physics Communications, Vol. 185, No. 4, 27.12.2013, p. 1207-1216.

Research output: Contribution to journalArticle

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