Quasioptimality of maximum-volume cross interpolation of tensors
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[1] White,et al. Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.
[2] Eugene E. Tyrtyshnikov,et al. Cross approximation in tensor electron density computations , 2010, Numer. Linear Algebra Appl..
[3] Petros Drineas,et al. FAST MONTE CARLO ALGORITHMS FOR MATRICES III: COMPUTING A COMPRESSED APPROXIMATE MATRIX DECOMPOSITION∗ , 2004 .
[4] О. С. Лебедева. Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT format , 2011 .
[5] Ivan Oseledets,et al. Tensor-Train Decomposition , 2011, SIAM J. Sci. Comput..
[6] Östlund,et al. Thermodynamic limit of density matrix renormalization. , 1995, Physical review letters.
[7] S. V. Dolgov,et al. ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ , 2014 .
[8] Y. Maday,et al. Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations , 2008, 0811.0474.
[9] Elías Cueto,et al. Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions , 2012, International journal for numerical methods in biomedical engineering.
[10] S. Dolgov. TT-GMRES: solution to a linear system in the structured tensor format , 2012, 1206.5512.
[11] Ivan V. Oseledets,et al. Fast adaptive interpolation of multi-dimensional arrays in tensor train format , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.
[12] M. Fannes,et al. Finitely correlated states on quantum spin chains , 1992 .
[13] Francisco Chinesta,et al. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids , 2006 .
[14] W. K. Hastings,et al. Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .
[15] Thomas Huckle,et al. Subspace Iteration Methods in terms of Matrix Product States , 2012 .
[16] W. Hackbusch. Tensor Spaces and Numerical Tensor Calculus , 2012, Springer Series in Computational Mathematics.
[17] Daniel Kressner,et al. Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems , 2011, SIAM J. Matrix Anal. Appl..
[18] Vladimir A. Kazeev,et al. Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity , 2013, SIAM J. Sci. Comput..
[19] Reinhold Schneider,et al. The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format , 2012, SIAM J. Sci. Comput..
[20] Lars Grasedyck,et al. F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig a Projection Method to Solve Linear Systems in Tensor Format a Projection Method to Solve Linear Systems in Tensor Format , 2022 .
[21] B. Khoromskij. Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances , 2012 .
[22] Wolfgang Dahmen,et al. Convergence Rates for Greedy Algorithms in Reduced Basis Methods , 2010, SIAM J. Math. Anal..
[23] E. Tyrtyshnikov. Kronecker-product approximations for some function-related matrices , 2004 .
[24] John J. Bartholdi,et al. A good submatrix is hard to find , 1982, Oper. Res. Lett..
[25] Eugene E. Tyrtyshnikov,et al. Quasioptimality of skeleton approximation of a matrix in the Chebyshev norm , 2011 .
[26] Daniel Kressner,et al. Krylov Subspace Methods for Linear Systems with Tensor Product Structure , 2010, SIAM J. Matrix Anal. Appl..
[27] Mark Coppejans,et al. Breaking the Curse of Dimensionality , 2000 .
[28] Lars Grasedyck,et al. Hierarchical Singular Value Decomposition of Tensors , 2010, SIAM J. Matrix Anal. Appl..
[29] Boris N. Khoromskij,et al. Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs , 2011, SIAM J. Sci. Comput..
[30] S. Goreinov,et al. The maximum-volume concept in approximation by low-rank matrices , 2001 .
[31] H. Bungartz,et al. Sparse grids , 2004, Acta Numerica.
[32] Markus Weimar. Breaking the curse of dimensionality , 2015 .
[33] Vladimir Temlyakov,et al. CAMBRIDGE MONOGRAPHS ON APPLIED AND COMPUTATIONAL MATHEMATICS , 2022 .
[34] S. Goreinov,et al. How to find a good submatrix , 2010 .
[35] Eric Jeckelmann. Dynamical density-matrix renormalization-group method , 2002 .
[36] Eugene E. Tyrtyshnikov,et al. Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time , 2008, SIAM J. Matrix Anal. Appl..
[37] U. Schollwoeck. The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.
[38] Eugene E. Tyrtyshnikov,et al. Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions , 2009, SIAM J. Sci. Comput..
[39] W. Hackbusch,et al. A New Scheme for the Tensor Representation , 2009 .
[40] J. Ballani,et al. Black box approximation of tensors in hierarchical Tucker format , 2013 .
[41] Daniel Kressner,et al. A literature survey of low‐rank tensor approximation techniques , 2013, 1302.7121.
[42] Lei Tang,et al. Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations , 2011, SIAM J. Sci. Comput..
[43] André Uschmajew,et al. On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format , 2013, SIAM J. Numer. Anal..
[44] E. Tyrtyshnikov,et al. TT-cross approximation for multidimensional arrays , 2010 .
[45] Mario Bebendorf,et al. Separation of Variables for Function Generated High-Order Tensors , 2014, J. Sci. Comput..
[46] Virginie Ehrlacher,et al. Convergence of a greedy algorithm for high-dimensional convex nonlinear problems , 2010, 1004.0095.
[47] A. Uschmajew,et al. LOCAL CONVERGENCE OF ALTERNATING SCHEMES FOR OPTIMIZATION OF CONVEX PROBLEMS IN THE TT FORMAT , 2011 .
[48] White,et al. Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.
[49] Ivan V. Oseledets,et al. DMRG Approach to Fast Linear Algebra in the TT-Format , 2011, Comput. Methods Appl. Math..
[50] Boris N. Khoromskij,et al. Superfast Fourier Transform Using QTT Approximation , 2012 .
[51] S. V. Dolgov,et al. Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm , 2013, ENUMATH.
[52] E. Tyrtyshnikov. Tensor approximations of matrices generated by asymptotically smooth functions , 2003 .
[53] J. Zittartz,et al. Matrix Product Ground States for One-Dimensional Spin-1 Quantum Antiferromagnets , 1993, cond-mat/9307028.
[54] I. Oseledets. Constructive Representation of Functions in Low-Rank Tensor Formats , 2012, Constructive Approximation.
[55] Yu-An Chen,et al. Density matrix renormalization group , 2014 .
[56] Ivan V. Oseledets,et al. Solution of Linear Systems and Matrix Inversion in the TT-Format , 2012, SIAM J. Sci. Comput..
[57] Jan Schneider-Barnes,et al. Error estimates for two-dimensional cross approximation , 2010, J. Approx. Theory.
[58] Boris N. Khoromskij,et al. Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs , 2010, Comput. Methods Appl. Math..
[59] B. Khoromskij. O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling , 2011 .
[60] Petros Drineas,et al. Tensor-CUR decompositions for tensor-based data , 2006, KDD '06.
[61] Severnyi Kavkaz. Pseudo-Skeleton Approximations by Matrices of Maximal Volume , 2022 .
[62] Hans-Joachim Bungartz,et al. Acta Numerica 2004: Sparse grids , 2004 .
[63] S. Goreinov,et al. Pseudo-skeleton approximations by matrices of maximal volume , 1997 .
[64] Daniel Kressner,et al. Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems , 2011, Comput. Methods Appl. Math..
[65] Boris N. Khoromskij,et al. Computation of extreme eigenvalues in higher dimensions using block tensor train format , 2013, Comput. Phys. Commun..
[66] Andrea Barth,et al. Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients , 2011, Numerische Mathematik.
[67] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[68] Eugene E. Tyrtyshnikov,et al. Incomplete Cross Approximation in the Mosaic-Skeleton Method , 2000, Computing.
[69] S. Goreinov,et al. A Theory of Pseudoskeleton Approximations , 1997 .
[70] T. A. Porsching,et al. Estimation of the error in the reduced basis method solution of nonlinear equations , 1985 .
[71] Mario Bebendorf,et al. Approximation of boundary element matrices , 2000, Numerische Mathematik.