Corrected one-site density matrix renormalization group and alternating minimal energy algorithm

Sergey V. Dolgov, Dmitry V. Savostyanov

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT)/matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme with the auxiliary (e.g. gradient) information, which substantially improves the convergence in many difficult cases. Being conceptually close, these methods have different derivation, implementation, theoretical and practical properties. We emphasize the differences, and reproduce the numerical example to compare the performance of two algorithms.

LanguageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications - ENUMATH 2013
EditorsA. Abdulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso
Place of PublicationCham, Switzerland
PublisherSpringer International Publishing
Pages335-343
Number of pages9
ISBN (Print)9783319107042
DOIs
StatusPublished - 1 Jan 2015

Publication series

NameLecture Notes in Computational Science and Engineering
Volume103

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Dolgov, S. V., & Savostyanov, D. V. (2015). Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. In A. Abdulle, S. Deparis, D. Kressner, F. Nobile, & M. Picasso (Eds.), Numerical Mathematics and Advanced Applications - ENUMATH 2013 (pp. 335-343). (Lecture Notes in Computational Science and Engineering; Vol. 103). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-319-10705-9_33

Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. / Dolgov, Sergey V.; Savostyanov, Dmitry V.

Numerical Mathematics and Advanced Applications - ENUMATH 2013. ed. / A. Abdulle; S. Deparis; D. Kressner; F. Nobile; M. Picasso. Cham, Switzerland : Springer International Publishing, 2015. p. 335-343 (Lecture Notes in Computational Science and Engineering; Vol. 103).

Research output: Chapter in Book/Report/Conference proceedingChapter

Dolgov, SV & Savostyanov, DV 2015, Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. in A Abdulle, S Deparis, D Kressner, F Nobile & M Picasso (eds), Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol. 103, Springer International Publishing, Cham, Switzerland, pp. 335-343. https://doi.org/10.1007/978-3-319-10705-9_33
Dolgov SV, Savostyanov DV. Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. In Abdulle A, Deparis S, Kressner D, Nobile F, Picasso M, editors, Numerical Mathematics and Advanced Applications - ENUMATH 2013. Cham, Switzerland: Springer International Publishing. 2015. p. 335-343. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-10705-9_33
Dolgov, Sergey V. ; Savostyanov, Dmitry V. / Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. Numerical Mathematics and Advanced Applications - ENUMATH 2013. editor / A. Abdulle ; S. Deparis ; D. Kressner ; F. Nobile ; M. Picasso. Cham, Switzerland : Springer International Publishing, 2015. pp. 335-343 (Lecture Notes in Computational Science and Engineering).
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