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

Sergey V. Dolgov, Dmitry V. Savostyanov

Research output: Chapter or section in a book/report/conference proceedingChapter or section

10 Citations (SciVal)


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.

Original 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
Number of pages9
ISBN (Print)9783319107042
Publication statusPublished - 1 Jan 2015

Publication series

NameLecture Notes in Computational Science and Engineering

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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