Tensor-Train Decomposition
暂无分享,去创建一个
[1] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[2] Eugene E. Tyrtyshnikov,et al. Linear algebra for tensor problems , 2009, Computing.
[3] Raúl Tempone,et al. Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations , 2004, SIAM J. Numer. Anal..
[4] Jonas Persson,et al. Pricing European multi-asset options using a space-time adaptive FD-method , 2007 .
[5] Pierre Comon,et al. Tensor Decompositions, State of the Art and Applications , 2002 .
[6] Boris N. Khoromskij,et al. Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays , 2009, SIAM J. Sci. Comput..
[7] R. Bro. PARAFAC. Tutorial and applications , 1997 .
[8] BabuskaIvo,et al. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2007 .
[9] Martin J. Mohlenkamp,et al. Numerical operator calculus in higher dimensions , 2002, Proceedings of the National Academy of Sciences of the United States of America.
[10] Mark Coppejans,et al. Breaking the Curse of Dimensionality , 2000 .
[11] Johan Håstad,et al. Tensor Rank is NP-Complete , 1989, ICALP.
[12] C. Lubich. From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis , 2008 .
[13] Ivan Oseledets,et al. QTT approximation of elliptic solution operators in higher dimensions , 2011 .
[14] Lars Grasedyck,et al. Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure , 2004, Computing.
[15] W. Hackbusch,et al. A New Scheme for the Tensor Representation , 2009 .
[16] Fabio Nobile,et al. A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..
[17] H. Meyer,et al. Benchmark calculations on high-dimensional Henon–Heiles potentials with the multi-configuration time dependent Hartree (MCTDH) method , 2002 .
[18] E. Tyrtyshnikov. Tensor approximations of matrices generated by asymptotically smooth functions , 2003 .
[19] Richard A. Harshman,et al. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .
[20] Boris N. Khoromskij,et al. Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions , 2005, Computing.
[21] Henryk Wozniakowski,et al. When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals? , 1998, J. Complex..
[22] Joos Vandewalle,et al. On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..
[23] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[24] Lars Grasedyck,et al. Hierarchical Singular Value Decomposition of Tensors , 2010, SIAM J. Matrix Anal. Appl..
[25] Fabio Nobile,et al. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2007, SIAM Rev..
[26] Ivan V. Oseledets,et al. Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case , 2010, SIAM J. Sci. Comput..
[27] Martin J. Mohlenkamp,et al. Algorithms for Numerical Analysis in High Dimensions , 2005, SIAM J. Sci. Comput..
[28] Boris N. Khoromskij,et al. Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators , 2005, Computing.
[29] Ivan Oseledets,et al. Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions , 2009 .
[30] E. Tyrtyshnikov,et al. TT-cross approximation for multidimensional arrays , 2010 .
[31] Joos Vandewalle,et al. A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..
[32] Boris N. Khoromskij,et al. Numerical Solution of the Hartree - Fock Equation in Multilevel Tensor-Structured Format , 2011, SIAM J. Sci. Comput..
[33] L. Tucker,et al. Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.
[34] Eugene E. Tyrtyshnikov,et al. Approximate multiplication of tensor matrices based on the individual filtering of factors , 2009 .
[35] Eugene E. Tyrtyshnikov,et al. Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions , 2009, SIAM J. Sci. Comput..
[36] Ian H. Sloan,et al. Why Are High-Dimensional Finance Problems Often of Low Effective Dimension? , 2005, SIAM J. Sci. Comput..
[37] Ivan Oseledets,et al. Tensor Structured Iterative Solution of Elliptic Problems with Jumping Coefficients , 2010 .
[38] Oriol Vendrell,et al. Full-dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. I. Hamiltonian setup and analysis of the ground vibrational state. , 2007, The Journal of chemical physics.
[39] J. Chang,et al. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .
[40] W. Dur,et al. Concatenated tensor network states , 2009, 0904.1925.
[41] C. Loan,et al. Approximation with Kronecker Products , 1992 .
[42] Eugene E. Tyrtyshnikov,et al. Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time , 2008, SIAM J. Matrix Anal. Appl..