Calculating vibrational spectra of molecules using tensor train decomposition

Grid-based electronic structure calculations: The tensor decomposition approach

(2016) M.V. Rakhuba et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fitting high-dimensional potential energy surface using active subspace and tensor train (AS+TT) method

(2015) Vitaly Baranov et al.   JOURNAL OF CHEMICAL PHYSICS

Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms

(2015) Phillip S. Thomas et al.   JOURNAL OF PHYSICAL CHEMISTRY A

Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation

(2015) M. V. Rakhuba et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Computation of extreme eigenvalues in higher dimensions using block tensor train format

(2014) S.V. Dolgov et al.   COMPUTER PHYSICS COMMUNICATIONS

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

(2014) M. Billaud-Friess et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices

(2014) Arnaud Leclerc et al.   JOURNAL OF CHEMICAL PHYSICS

Quasioptimality of maximum-volume cross interpolation of tensors

(2014) Dmitry V. Savostyanov   LINEAR ALGEBRA AND ITS APPLICATIONS

Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

(2014) Sergey V. Dolgov et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

TT-GMRES: solution to a linear system in the structured tensor format

(2013) S. V. Dolgov   RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING

Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

(2013) Daniel Kressner et al.   Computational Methods in Applied Mathematics

Variational Numerical Renormalization Group: Bridging the Gap between NRG and Density Matrix Renormalization Group

(2012) Iztok Pižorn et al.   PHYSICAL REVIEW LETTERS

The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format

(2012) Sebastian Holtz et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D

(2011) Gustavo Avila et al.   JOURNAL OF CHEMICAL PHYSICS

Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4

(2011) Gustavo Avila et al.   JOURNAL OF CHEMICAL PHYSICS

Use of tensor formats in elliptic eigenvalue problems

(2011) Wolfgang Hackbusch et al.   NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format

(2011) O. S. Lebedeva   RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING

Tensor-Train Decomposition

(2011) I. V. Oseledets   SIAM JOURNAL ON SCIENTIFIC COMPUTING

The density-matrix renormalization group in the age of matrix product states

(2010) Ulrich Schollwöck   ANNALS OF PHYSICS

Hierarchical Singular Value Decomposition of Tensors

(2010) Lars Grasedyck   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Tensor-Structured Preconditioners and Approximate Inverse of Elliptic Operators in ℝ d

(2009) Boris N. Khoromskij   CONSTRUCTIVE APPROXIMATION

TT-cross approximation for multidimensional arrays

(2009) Ivan Oseledets et al.   LINEAR ALGEBRA AND ITS APPLICATIONS

Multivariate Regression and Machine Learning with Sums of Separable Functions

(2009) Gregory Beylkin et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Tensor Decompositions and Applications

(2009) Tamara G. Kolda et al.   SIAM REVIEW

Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

(2008) Vin de Silva et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS