On the Dirac–Frenkel Variational Principle on Tensor Banach Spaces

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

[2]  Petr Hájek,et al.  Smooth analysis in Banach spaces , 2014 .

[3]  Tobias Jahnke,et al.  On the approximation of high-dimensional differential equations in the hierarchical Tucker format , 2014 .

[4]  Bart Vandereycken,et al.  The geometry of algorithms using hierarchical tensors , 2013, Linear Algebra and its Applications.

[5]  Antonio Falcó,et al.  On Minimal Subspaces in Tensor Representations , 2012, Found. Comput. Math..

[6]  F. Verstraete,et al.  Geometry of Matrix Product States: metric, parallel transport and curvature , 2012, 1210.7710.

[7]  Harald Upmeier,et al.  Symmetric Banach Manifolds and Jordan C*-Algebras , 2012 .

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

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

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

[11]  Petr Hájek,et al.  Banach Space Theory , 2011 .

[12]  Othmar Koch,et al.  Dynamical Tensor Approximation , 2010, SIAM J. Matrix Anal. Appl..

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

[14]  E. Tyrtyshnikov,et al.  TT-cross approximation for multidimensional arrays , 2010 .

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

[16]  Ivan Oseledets,et al.  A new tensor decomposition , 2009 .

[17]  Jim Hefferon,et al.  Linear Algebra , 2012 .

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

[19]  F. Verstraete,et al.  Matrix product states represent ground states faithfully , 2005, cond-mat/0505140.

[20]  Ya.I. Alber.  James orthogonality and orthogonal decompositions of Banach spaces , 2005 .

[21]  Daniel Beltita,et al.  Smooth homogeneous structures in operator theory , 2005 .

[22]  H. Wimmer,et al.  Estimates for projections in Banach spaces and existence of direct complements , 2005 .

[23]  BARRY SIMON,et al.  Uniform Crossnorms , 2004 .

[24]  G. Vidal.  Efficient classical simulation of slightly entangled quantum computations. , 2003, Physical review letters.

[25]  Wataru Takahashi,et al.  Strong Convergence of a Proximal-Type Algorithm in a Banach Space , 2002, SIAM J. Optim..

[26]  S. Lang.  Differential and Riemannian Manifolds , 1996 .

[27]  I. Ciorǎnescu.  Geometry of banach spaces, duality mappings, and nonlinear problems , 1990 .

[28]  Will Light,et al.  Approximation Theory in Tensor Product Spaces , 1985 .

[29]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[30]  A. Douady,et al.  Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné , 1966 .

[31]  R. C. James.  Weakly compact sets , 1964 .

[32]  D. R. Hartree,et al.  The calculation of atomic structures , 1959 .

[33]  E. Schmidt.  Zur Theorie der linearen und nichtlinearen Integralgleichungen , 1907 .