Keyword

tensor train format

Description: A tensor decomposition that represents a high-dimensional array as a chain of smaller core tensors, used in numerical computing and optimization.

Primary topic: Tensor decomposition and applications (63%)

OpenAlex ID: keywords/tensor-train-format

Tensorizing Neural Networks

2015 · Novikov, Alexander, Podoprikhin, Dmitry, et al. · arXiv (Cornell University) · 657

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

2012 · Sebastian Holtz, Thorsten Rohwedder, et al. · SIAM Journal on Scientific Computing · 336

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

2012 · I. V. Oseledets, S. V. Dolgov · SIAM Journal on Scientific Computing · 187

Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors

2013 · Christian Lubich, Thorsten Rohwedder, et al. · SIAM Journal on Matrix Analysis and Applications · 162

Low rank tensor recovery via iterative hard thresholding

2017 · Holger Rauhut, Reinhold Schneider, et al. · Linear Algebra and its Applications · 140

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Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics

2017 · Samuel M. Greene, Victor S. Batista · Journal of Chemical Theory and Computation · 130

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Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation

2012 · S. V. Dolgov, B. N. Khoromskij, et al. · SIAM Journal on Scientific Computing · 126

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

2012 · Vladimir A. Kazeev, Boris N. Khoromskij · SIAM Journal on Matrix Analysis and Applications · 118

Black box approximation of tensors in hierarchical Tucker format

2011 · Jonas Ballani, Lars Grasedyck, et al. · Linear Algebra and its Applications · 112

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Constructive Representation of Functions in Low-Rank Tensor Formats

2012 · I. V. Oseledets · Constructive Approximation · 111

Compressing recurrent neural network with tensor train

2017 · Andros Tjandra, Sakriani Sakti, et al. · 109

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Fast adaptive interpolation of multi-dimensional arrays in tensor train format

2011 · Dmitry Savostyanov, Ivan Oseledets · 102

On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format

2013 · Thorsten Rohwedder, André Uschmajew · SIAM Journal on Numerical Analysis · 98

Riemannian Optimization for High-Dimensional Tensor Completion

2016 · Michael Steinlechner · SIAM Journal on Scientific Computing · 84

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

2013 · S. V. Dolgov · Russian Journal of Numerical Analysis and Mathematical Modelling · 79

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

2013 · Vladimir A. Kazeev, Boris N. Khoromskij, et al. · SIAM Journal on Scientific Computing · 78

Quasioptimality of maximum-volume cross interpolation of tensors

2014 · Dmitry V. Savostyanov · Linear Algebra and its Applications · 76

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A Semi-Lagrangian Vlasov Solver in Tensor Train Format

2015 · Katharina Kormann · SIAM Journal on Scientific Computing · 70

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Simultaneous state‐time approximation of the chemical master equation using tensor product formats

2014 · Sergey Dolgov, Boris Khoromskij · Numerical Linear Algebra with Applications · 68

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Variants of Alternating Least Squares Tensor Completion in the Tensor Train Format

2015 · Lars Grasedyck, Melanie Kluge, et al. · SIAM Journal on Scientific Computing · 67

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

2014 · Daniel Kressner, Michael Steinlechner, et al. · SIAM Journal on Scientific Computing · 67

DMRG Approach to Fast Linear Algebra in the TT-Format

2011 · Ivan Oseledets · Computational Methods in Applied Mathematics · 62

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On Minimal Subspaces in Tensor Representations

2012 · Antonio Falcó, Wolfgang Hackbusch · Foundations of Computational Mathematics · 60

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Exponential machines

2018 · A. Novikov, M. Trofimov, et al. · Bulletin of the Polish Academy of Sciences Technical Sciences · 54

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Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure

2016 · Daniel Kressner, Michael Steinlechner, et al. · SIAM Journal on Scientific Computing · 50

Works count: 407

Citation count: 4,981