### 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 |
---|---|

Pages (from-to) | 335-343 |

Number of pages | 9 |

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

Volume | 103 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

## Fingerprint Dive into the research topics of 'Corrected one-site density matrix renormalization group and alternating minimal energy algorithm'. Together they form a unique fingerprint.

## Cite this

Dolgov, S. V., & Savostyanov, D. V. (2015). Corrected one-site density matrix renormalization group and alternating minimal energy algorithm.

*Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering*,*103*, 335-343. https://doi.org/10.1007/978-3-319-10705-9_33