Ivan Oseledets
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Tensor-Train Decomposition
IV Oseledets
SIAM Journal on Scientific Computing 33, 2295-2317, 2011
Speeding-up convolutional neural networks using fine-tuned cp-decomposition
V Lebedev, Y Ganin, M Rakhuba, I Oseledets, V Lempitsky
arXiv preprint arXiv:1412.6553, 2014
Breaking the curse of dimensionality, or how to use SVD in many dimensions
IV Oseledets, EE Tyrtyshnikov
SIAM Journal on Scientific Computing 31 (5), 3744-3759, 2009
TT-cross approximation for multidimensional arrays
I Oseledets, E Tyrtyshnikov
Linear Algebra and its Applications 432 (1), 70-88, 2010
Unifying time evolution and optimization with matrix product states
J Haegeman, C Lubich, I Oseledets, B Vandereycken, F Verstraete
Physical Review B 94 (16), 165116, 2016
Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions
A Cichocki, N Lee, I Oseledets, AH Phan, Q Zhao, DP Mandic
Foundations and Trends® in Machine Learning 9 (4-5), 249-429, 2016
Approximation of Matrices Using Tensor Decomposition
IV Oseledets
SIAM Journal on Matrix Analysis and Applications 31, 2130-2145, 2010
How to find a good submatrix
SA Goreinov, IV Oseledets, DV Savostyanov, EE Tyrtyshnikov, ...
Matrix Methods: Theory, Algorithms And Applications: Dedicated to the Memory …, 2010
Tucker dimensionality reduction of three-dimensional arrays in linear time
IV Oseledets, DV Savostianov, EE Tyrtyshnikov
SIAM Journal on Matrix Analysis and Applications 30 (3), 939-956, 2008
Solution of linear systems and matrix inversion in the TT-format
IV Oseledets, SV Dolgov
SIAM Journal on Scientific Computing 34 (5), A2718-A2739, 2012
Tensor networks for dimensionality reduction and large-scale optimizations. part 2 applications and future perspectives
A Cichocki, AH Phan, Q Zhao, N Lee, IV Oseledets, M Sugiyama, ...
arXiv preprint arXiv:1708.09165, 2017
Fast solution of multi-dimensional parabolic problems in the tensor train/quantized tensor train-format with initial application to the Fokker-Planck equation.
SV Dolgov, BN Khoromskij, IV Oseledets
SIAM Journal on Scientific Computing 34 (6), A3016–A3038, 2012
Time integration of tensor trains
C Lubich, IV Oseledets, B Vandereycken
SIAM Journal on Numerical Analysis 53 (2), 917-941, 2015
Fast adaptive interpolation of multi-dimensional arrays in tensor train format
D Savostyanov, I Oseledets
The 2011 International Workshop on Multidimensional (nD) Systems, 1-8, 2011
Enabling high-dimensional hierarchical uncertainty quantification by ANOVA and tensor-train decomposition
Z Zhang, X Yang, IV Oseledets, GE Karniadakis, L Daniel
IEEE Transactions on Computer-Aided Design of Integrated Circuits and …, 2014
Computation of extreme eigenvalues in higher dimensions using block tensor train format
SV Dolgov, BN Khoromskij, IV Oseledets, DV Savostyanov
Computer Physics Communications 185 (4), 1207-1216, 2014
A projector-splitting integrator for dynamical low-rank approximation
C Lubich, IV Oseledets
BIT Numerical Mathematics 54 (1), 171-188, 2014
Neural networks for topology optimization
I Sosnovik, I Oseledets
Russian Journal of Numerical Analysis and Mathematical Modelling 34 (4), 215-223, 2019
Tensor methods and recommender systems
E Frolov, I Oseledets
Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 7 (3 …, 2017
Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs
BN Khoromskij, I Oseledets
Computational methods in applied mathematics 10 (4), 376-394, 2010
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