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The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS).
An identity for the schur complement of a matrix ,
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Density matrix formulation for quantum renormalization groups ,
S. R. White, · 1992
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A geometric analysis of gaussian elimination. II ,
L. Neal and G. Poole, · 1992
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Matrix computations ,
G. H. Golub and C. F. Van Loan, · 1996
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Potts model with long-range interactions in one dimension ,
E. Bayong, H. T. Diep and V. Dotsenko, · 1999
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On the existence and computation of rank-revealing LU factorizations ,
C.-T. Pan, · 2000
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Approximation of boundary element matrices ,
M. Bebendorf, · 2000
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Incomplete cross approximation in the mosaic-skeleton method ,
E. Tyrtyshnikov, · 2000
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The rook’s pivoting strategy ,
G. Poole and L. Neal, · 2000
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Criticality in one dimension with inverse square-law potentials ,
E. Luijten and H. Meßingfeld, · 2001
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Adaptive low-rank approximation of collocation matrices ,
M. Bebendorf and S. Rjasanow, · 2003
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A Schur complement approach to a general extrapolation algorithm ,
C. Brezinski and M. Redivo-Zaglia, · 2003
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Strong rank revealing LU factorizations ,
L. Miranian and M. Gu, · 2003
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Renormalization algorithms for quantum-many body systems in two and higher dimensions ,
F. Verstraete and J. I. Cirac, · 2004
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Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation ,
M. Bebendorf and R. Grzhibovskis, · 2006
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Tucker dimensionality reduction of three-dimensional arrays in linear time ,
I. V. Oseledets, D. V. Savostianov and E. E. Tyrtyshnikov, · 2008
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Order-n cluster monte carlo method for spin systems with long-range interactions ,
K. Fukui and S. Todo, · 2008
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TT-cross approximation for multidimensional arrays ,
I. Oseledets and E. Tyrtyshnikov, · 2009
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Approximation of matrices with logarithmic number of parameters ,
I. V. Oseledets, · 2009
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The density-matrix renormalization group in the age of matrix product states ,
U. Schollwöck, · 2010
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Error estimates for two-dimensional cross approximation ,
J. Schneider, · 2010
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Approximation of 2 d × 2 d 2^{d}\times 2^{d} matrices using tensor decomposition ,
I. V. Oseledets, · 2010
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Minimally entangled typical thermal state algorithms ,
E. M. Stoudenmire and S. R. White, · 2010
Cited alongside, same era.
TT-toolbox: Matlab implementation of tensor train decomposition ,
I. Oseledets, S. V. Dolgov, A. Boyko, D. Savostyanov, A. Novikov and T. Mach, · 2011
Cited alongside, same era.
Tensor-train decomposition ,
I. V. Oseledets, · 2011
Cited alongside, same era.
Fast adaptive interpolation of multi-dimensional arrays in tensor train format ,
D. Savostyanov and I. Oseledets, · 2011
Cited alongside, same era.
Adaptive cross approximation of multivariate functions ,
M. Bebendorf, · 2011
Cited alongside, same era.
Quasioptimality of skeleton approximation of a matrix in the Chebyshev norm ,
S. A. Goreinov and E. E. Tyrtyshnikov, · 2011
Cited alongside, same era.
Learning Feynman diagrams with tensor trains ,
Y. Núñez Fernández, M. Jeannin, P. T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet and X. Waintal, · 2022
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TTOpt: A maximum volume quantized tensor train-based optimization and its application to reinforcement learning ,
K. Sozykin, A. Chertkov, R. Schutski, A.-H. Phan, A. Cichocki and I. Oseledets, · 2022
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A quantum inspired approach to exploit turbulence structures ,
N. Gourianov, M. Lubasch, S. Dolgov, Q. Y. van den Berg, H. Babaee, P. Givi, M. Kiffner and D. Jaksch, · 2022
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Exploiting the structure of turbulence with tensor networks ,
N. Gourianov, · 2022
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Quantum-inspired method for solving the vlasov-poisson equations ,
E. Ye and N. F. G. Loureiro, · 2022
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The ITensor software library for tensor network calculations ,
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ttpy: Python implementation of the TT-toolbox ,
I. Oseledets, · 2012
Cited alongside, same era.
Superfast fourier transform using QTT approximation ,
S. Dolgov, B. Khoromskij and D. Savostyanov, · 2012
Cited alongside, same era.
A practical introduction to tensor networks: Matrix product states and projected entangled pair states ,
R. Orús, · 2014
Cited alongside, same era.
Quasioptimality of maximum-volume cross interpolation of tensors ,
D. V. Savostyanov, · 2014
Cited alongside, same era.
Scale invariance and efficient classical simulation of the quantum fourier transform ,
K. J. Woolfe, C. D. Hill and L. C. L. Hollenberg, · 2014
Cited alongside, same era.
Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms ,
G. K. Chan, A. Keselman, N. Nakatani, Z. Li and S. R. White, · 2016
Cited alongside, same era.
M. Fishman, S. R. White and E. M. Stoudenmire, · 2022
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Density Matrix and Tensor Network Renormalization ,
T. Xiang, · 2023
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Tensorized orbitals for computational chemistry ,
N. Jolly, Y. Núñez Fernández and X. Waintal, · 2023
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Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains ,
H. Shinaoka, M. Wallerberger, Y. Murakami, K. Nogaki, R. Sakurai, P. Werner and A. Kauch, · 2023
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Complete quantum-inspired framework for computational fluid dynamics ,
R. D. Peddinti, S. Pisoni, A. Marini, P. Lott, H. Argentieri, E. Tiunov and L. Aolita, · 2023
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Tensor train continuous time solver for quantum impurity models ,
A. Erpenbeck, W.-T. Lin, T. Blommel, L. Zhang, S. Iskakov, L. Bernheimer, Y. Núñez Fernández, G. Cohen, O. Parcollet, X. Waintal and E. Gull, · 2023
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Quantum fourier transform has small entanglement ,
J. Chen, E. Stoudenmire and S. R. White, · 2023
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Quantics tensor cross interpolation for high-resolution parsimonious representations of multivariate functions ,
M. K. Ritter, Y. Núñez Fernández, M. Wallerberger, J. von Delft, H. Shinaoka and X. Waintal, · 2024
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Learning parameter dependence for fourier-based option pricing with tensor networks (2024),
R. Sakurai, H. Takahashi and K. Miyamoto, · 2024
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Compactness of quantics tensor train representations of local imaginary-time propagators ,
H. Takahashi, R. Sakurai and H. Shinaoka, · 2024
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Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models ,
H. Ishida, N. Okada, S. Hoshino and H. Shinaoka, · 2024
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Nonequilibrium diagrammatic many-body simulations with quantics tensor trains ,
M. Murray, H. Shinaoka and P. Werner, · 2024
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High-resolution nonequilibrium g w gw calculations based on quantics tensor trains ,
M. Środa, K. Inayoshi, H. Shinaoka and P. Werner, · 2024
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Learning tensor trains from noisy functions with application to quantum simulation (2024),
K. Sakaue, H. Shinaoka and R. Sakurai, · 2024
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Direct interpolative construction of the discrete fourier transform as a matrix product operator ,
J. Chen and M. Lindsey, · 2024
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private communication (2024)
Y. Yu, · 2024
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