Parallel Algorithms for Tensor Train Arithmetic

PLANC

(2021) Srinivas Eswar et al.   ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE

Low‐rank solution of an optimal control problem constrained by random Navier‐Stokes equations

(2020) Peter Benner et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

TuckerMPI

(2020) Grey Ballard et al.   ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE

ADTT: A Highly Efficient Distributed Tensor-Train Decomposition Method for IIoT Big Data

(2020) Xiaokang Wang et al.   IEEE Transactions on Industrial Informatics

Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations

(2017) Sergey Dolgov et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Recompression of Hadamard Products of Tensors in Tucker Format

(2017) Daniel Kressner et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

(2016) F. Bonizzoni et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data

(2016) Peter Benner et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Reconstructing Householder vectors from Tall-Skinny QR

(2015) G. Ballard et al.   JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

(2015) Peter Benner et al.   SIAM REVIEW

Low-Rank Tensor Approximation for High-Order Correlation Functions of Gaussian Random Fields

(2015) Daniel Kressner et al.   SIAM-ASA Journal on Uncertainty Quantification

A massively parallel tensor contraction framework for coupled-cluster computations

(2014) Edgar Solomonik et al.   JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING

Exact NMR simulation of protein-size spin systems using tensor train formalism

(2014) D. V. Savostyanov et al.   PHYSICAL REVIEW B

Communication lower bounds and optimal algorithms for numerical linear algebra

(2014) G. Ballard et al.   ACTA NUMERICA

Fast Alternating LS Algorithms for High Order CANDECOMP/PARAFAC Tensor Factorizations

(2013) Anh-Huy Phan et al.   IEEE TRANSACTIONS ON SIGNAL PROCESSING

Real-space parallel density matrix renormalization group

(2013) E. M. Stoudenmire et al.   PHYSICAL REVIEW B

Block Tensor Unfoldings

(2012) Stefan Ragnarsson et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Communication-optimal Parallel and Sequential QR and LU Factorizations

(2012) James Demmel et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling

(2011) Boris N. Khoromskij   CONSTRUCTIVE APPROXIMATION

Tensor-Train Decomposition

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

Krylov Subspace Methods for Linear Systems with Tensor Product Structure

(2010) Daniel Kressner et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

A New Scheme for the Tensor Representation

(2009) W. Hackbusch et al.   JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

TT-cross approximation for multidimensional arrays

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

Tensor Decompositions and Applications

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