Fundamental tensor operations for large-scale data analysis using tensor network formats

Regularized Computation of Approximate Pseudoinverse of Large Matrices Using Low-Rank Tensor Train Decompositions

(2016) Namgil Lee et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format

(2015) Namgil Lee et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

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

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

Breaking the Curse of Dimensionality Using Decompositions of Incomplete Tensors: Tensor-based scientific computing in big data analysis

(2014) Nico Vervliet et al.   IEEE SIGNAL PROCESSING MAGAZINE

Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems

(2014) Daniel Kressner et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

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

Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity

(2013) Vladimir A. Kazeev et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

On Minimal Subspaces in Tensor Representations

(2012) Antonio Falcó et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse

(2012) Vladimir A. Kazeev et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

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

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

Solution of Linear Systems and Matrix Inversion in the TT-Format

(2012) I. V. Oseledets et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Tensors-structured numerical methods in scientific computing: Survey on recent advances

(2011) Boris N. Khoromskij   CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS

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

(2011) Boris N. Khoromskij   CONSTRUCTIVE APPROXIMATION

On manifolds of tensors of fixed TT-rank

(2011) Sebastian Holtz et al.   NUMERISCHE MATHEMATIK

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

Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition

(2010) I. V. Oseledets   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Hierarchical Singular Value Decomposition of Tensors

(2010) Lars Grasedyck   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

Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

(2009) I. V. Oseledets et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Tensor Decompositions and Applications

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