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

Sergey V. Dolgov, Dmitry V. Savostyanov

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)335-343
Number of pages9
JournalNumerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering
Volume103
DOIs
Publication statusPublished - 1 Jan 2015

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