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

Sergey V. Dolgov; Dmitry V. Savostyanov

doi:10.1007/978-3-319-10705-9_33

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

Sergey V. Dolgov, Dmitry V. Savostyanov

Department of Mathematical Sciences

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

10 Citations (SciVal)

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 language	English
Title of host publication	Numerical Mathematics and Advanced Applications - ENUMATH 2013
Editors	A. Abdulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso
Place of Publication	Cham, Switzerland
Publisher	Springer International Publishing
Pages	335-343
Number of pages	9
ISBN (Print)	9783319107042
DOIs	https://doi.org/10.1007/978-3-319-10705-9_33
Publication status	Published - 1 Jan 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	103

ASJC Scopus subject areas

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

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10.1007/978-3-319-10705-9_33

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). 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 or section in a book/report/conference proceeding › Chapter or section

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). Epub 2014 Oct 31. doi: 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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Corrected one-site density matrix renormalization group and alternating minimal energy algorithm

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