Tensor methods in quantum chemistry

[1]  W. Hackbusch.  Tensor Spaces and Numerical Tensor Calculus , 2012, Springer Series in Computational Mathematics.

[2]  W. Hackbusch,et al.  A New Scheme for the Tensor Representation , 2009 .

[3]  Ors Legeza,et al.  Simulating strongly correlated quantum systems with tree tensor networks , 2010, 1006.3095.

[4]  Ivan V. Oseledets,et al.  Approximation of 2d˟2d Matrices Using Tensor Decomposition , 2010, SIAM J. Matrix Anal. Appl..

[5]  J. Sólyom,et al.  Optimizing the density-matrix renormalization group method using quantum information entropy , 2003 .

[6]  Martin J. Mohlenkamp,et al.  Algorithms for Numerical Analysis in High Dimensions , 2005, SIAM J. Sci. Comput..

[7]  Ivan Oseledets,et al.  Tensor-Train Decomposition , 2011, SIAM J. Sci. Comput..

[8]  U. Schollwoeck.  The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[9]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[10]  Christopher J. Hillar,et al.  Most Tensor Problems Are NP-Hard , 2009, JACM.

[11]  Antonio Falcó,et al.  Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces , 2011, Numerische Mathematik.

[12]  C. Lubich.  From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis , 2008 .

[13]  Reinhold Schneider,et al.  On manifolds of tensors of fixed TT-rank , 2012, Numerische Mathematik.

[14]  Virginie Ehrlacher,et al.  Convergence of a greedy algorithm for high-dimensional convex nonlinear problems , 2010, 1004.0095.

[15]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[16]  Yang Qi,et al.  On the geometry of tensor network states , 2011, Quantum Inf. Comput..

[17]  R. Schneider,et al.  The Alternating Linear Scheme for Tensor Optimisation in the TT Format , 2022 .

[18]  C. Bardos,et al.  Setting and Analysis of the Multi-configuration Time-dependent Hartree–Fock Equations , 2009, 0903.3647.

[19]  F. Verstraete,et al.  Complete-graph tensor network states: a new fermionic wave function ansatz for molecules , 2010, 1004.5303.

[20]  Lars Grasedyck,et al.  Hierarchical Singular Value Decomposition of Tensors , 2010, SIAM J. Matrix Anal. Appl..