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
SN - 1439-7358
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
ER -