TY - JOUR

T1 - Corrected one-site density matrix renormalization group and alternating minimal energy algorithm

AU - Dolgov, Sergey V.

AU - Savostyanov, Dmitry V.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84919797964&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-10705-9_33

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

M3 - Article

AN - SCOPUS:84919797964

VL - 103

SP - 335

EP - 343

JO - Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering

JF - Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering

SN - 1439-7358

ER -