[HTML][HTML] The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges
In the past two decades, the density matrix renormalization group (DMRG) has emerged as
an innovative new method in quantum chemistry relying on a theoretical framework very …
an innovative new method in quantum chemistry relying on a theoretical framework very …
A literature survey of low‐rank tensor approximation techniques
L Grasedyck, D Kressner, C Tobler - GAMM‐Mitteilungen, 2013 - Wiley Online Library
During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …
scientific computing to address large‐scale linear and multilinear algebra problems, which …
Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions
Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …
multidimensional data of exceedingly high volume, variety, and structural richness …
Supervised learning with tensor networks
E Stoudenmire, DJ Schwab - Advances in neural …, 2016 - proceedings.neurips.cc
Tensor networks are approximations of high-order tensors which are efficient to work with
and have been very successful for physics and mathematics applications. We demonstrate …
and have been very successful for physics and mathematics applications. We demonstrate …
Tensor ring decomposition
Tensor networks have in recent years emerged as the powerful tools for solving the large-
scale optimization problems. One of the most popular tensor network is tensor train (TT) …
scale optimization problems. One of the most popular tensor network is tensor train (TT) …
Efficient tensor completion for color image and video recovery: Low-rank tensor train
JA Bengua, HN Phien, HD Tuan… - IEEE Transactions on …, 2017 - ieeexplore.ieee.org
This paper proposes a novel approach to tensor completion, which recovers missing entries
of data represented by tensors. The approach is based on the tensor train (TT) rank, which is …
of data represented by tensors. The approach is based on the tensor train (TT) rank, which is …
Tensor networks for dimensionality reduction and large-scale optimization: Part 2 applications and future perspectives
Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …
[图书][B] Tensor spaces and numerical tensor calculus
W Hackbusch - 2012 - Springer
Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …
On the numerical approximation of the Perron-Frobenius and Koopman operator
Information about the behavior of dynamical systems can often be obtained by analyzing the
eigenvalues and corresponding eigenfunctions of linear operators associated with a …
eigenvalues and corresponding eigenfunctions of linear operators associated with a …
Modeling nonlinear systems using the tensor network B‐spline and the multi‐innovation identification theory
Y Wang, S Tang, M Deng - International Journal of Robust and …, 2022 - Wiley Online Library
The nonlinear autoregressive exogenous (NARX) model shows a strong expression
capacity for nonlinear systems since these systems have limited information about their …
capacity for nonlinear systems since these systems have limited information about their …