-
1
-
-
84884085211
-
-
University Press, Princeton, NJ
-
P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press, Princeton, NJ, 2008.
-
(2008)
Optimization Algorithms on Matrix Manifolds, Princeton
-
-
Absil, P.-A.1
Mahony, R.2
Sepulchre, R.3
-
2
-
-
0036494136
-
A Grassmann-Rayleigh quotient iteration for computing invariant subspaces
-
P. A. Absil, R. Mahony, R. Sepulchre, and P. Van Dooren, A Grassmann-Rayleigh quotient iteration for computing invariant subspaces, SIAM Rev., 44 (2002), pp. 57-73.
-
(2002)
SIAM Rev.
, vol.44
, pp. 57-73
-
-
Absil, P.A.1
Mahony, R.2
Sepulchre, R.3
Van Dooren, P.4
-
3
-
-
18344373359
-
Generalised meshes for quantum mechanical problems
-
D. Baye and P.-H. Heenen, Generalised meshes for quantum mechanical problems, J. Phys. A, 19 (1986), pp. 2041-2059.
-
(1986)
J. Phys. A
, vol.19
, pp. 2041-2059
-
-
Baye, D.1
Heenen, P.-H.2
-
4
-
-
0344845742
-
A subspace preconditioning algorithm for eigenvector/eigenvalue computation
-
J. H. Bramble, J. E. Pasciak, and A. V. Knyazev, A subspace preconditioning algorithm for eigenvector/eigenvalue computation, Adv. Comput. Math., 6 (1996), pp. 159-189.
-
(1996)
Adv. Comput. Math.
, vol.6
, pp. 159-189
-
-
Bramble, J.H.1
Pasciak, J.E.2
Knyazev, A.V.3
-
5
-
-
84871571335
-
Periodic Schrödinger operators with local defects and spectral pollution
-
E. Cances, V. Ehrlacher, and Y. Maday, Periodic Schrödinger operators with local defects and spectral pollution, SIAM J. Numer. Anal., 50 (2012), pp. 3016-3035.
-
(2012)
SIAM J. Numer. Anal.
, vol.50
, pp. 3016-3035
-
-
Cances, E.1
Ehrlacher, V.2
Maday, Y.3
-
6
-
-
84894609844
-
Computation of extreme eigenvalues in higher dimensions using block tensor train format
-
S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, and D. V. Savostyanov, Computation of extreme eigenvalues in higher dimensions using block tensor train format, Comput. Phys. Comm., 185 (2014), pp. 1207-1216.
-
(2014)
Comput. Phys. Comm.
, vol.185
, pp. 1207-1216
-
-
Dolgov, S.V.1
Khoromskij, B.N.2
Oseledets, I.V.3
Savostyanov, D.V.4
-
7
-
-
84857675961
-
Low-rank tensor structure of solutions to elliptic problems with jumping coefficients
-
S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, and E. E. Tyrtyshnikov, Low-rank tensor structure of solutions to elliptic problems with jumping coefficients, J. Comput. Math., 30 (2012), pp. 14-23.
-
(2012)
J. Comput. Math.
, vol.30
, pp. 14-23
-
-
Dolgov, S.V.1
Khoromskij, B.N.2
Oseledets, I.V.3
Tyrtyshnikov, E.E.4
-
11
-
-
0032216898
-
The geometry of algorithms with orthogonality constraints
-
A. Edelman, T. A. Arias, and S. T. Smith, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 303-353.
-
(1998)
SIAM J. Matrix Anal. Appl.
, vol.20
, pp. 303-353
-
-
Edelman, A.1
Arias, T.A.2
Smith, S.T.3
-
12
-
-
77953845148
-
Computing semiclassical quantum dynamics with Hagedorn wavepackets
-
E. Faou, V. Gradinaru, and C. Lubich, Computing semiclassical quantum dynamics with Hagedorn wavepackets, SIAM J. Sci. Comput., 31 (2009), pp. 3027-3041.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 3027-3041
-
-
Faou, E.1
Gradinaru, V.2
Lubich, C.3
-
13
-
-
3042756404
-
Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
-
L. Grasedyck, Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure, Computing, 72 (2004), pp. 247-265.
-
(2004)
Computing
, vol.72
, pp. 247-265
-
-
Grasedyck, L.1
-
14
-
-
77956032667
-
Hierarchical singular value decomposition of tensors
-
L. Grasedyck, Hierarchical singular value decomposition of tensors, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2029-2054.
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 2029-2054
-
-
Grasedyck, L.1
-
15
-
-
84892949294
-
A literature survey of low-rank tensor approximation techniques
-
L. Grasedyck, D. Kressner, and C. Tobler, A literature survey of low-rank tensor approximation techniques, GAMM Mitt. Ges. Angew. Math. Mech., 36 (2013), pp. 53-78.
-
(2013)
GAMM Mitt. Ges. Angew. Math. Mech.
, vol.36
, pp. 53-78
-
-
Grasedyck, L.1
Kressner, D.2
Tobler, C.3
-
16
-
-
41549129981
-
-
Technical report 4/2005, MPI MIS, Leipzig, Germany
-
W. Hackbusch, Entwicklungen nach Exponentialsummen, Technical report 4/2005, MPI MIS, Leipzig, Germany, 2010.
-
(2010)
Entwicklungen nach Exponentialsummen
-
-
Hackbusch, W.1
-
18
-
-
84855234730
-
Use of tensor formats in elliptic eigenvalue problems, Numer
-
W. Hackbusch, B. N. Khoromskij, S. A. Sauter, and E. E. Tyrtyshnikov, Use of tensor formats in elliptic eigenvalue problems, Numer. Linear Algebra Appl., 19 (2012), pp. 133-151.
-
(2012)
Linear Algebra Appl.
, vol.19
, pp. 133-151
-
-
Hackbusch, W.1
Khoromskij, B.N.2
Sauter, S.A.3
Tyrtyshnikov, E.E.4
-
19
-
-
77952289640
-
A new scheme for the tensor representation
-
W. Hackbusch and S. Kühn, A new scheme for the tensor representation, J. Fourier Anal. Appl., 15 (2009), pp. 706-722.
-
(2009)
J. Fourier Anal. Appl.
, vol.15
, pp. 706-722
-
-
Hackbusch, W.1
Kühn, S.2
-
20
-
-
11044224123
-
Multiresolution quantum chemistry: Basic theory and initial applications
-
R. J. Harrison, G. I. Fann, T. Yanai, Z. Gan, and G. Beylkin, Multiresolution quantum chemistry: Basic theory and initial applications, J. Chem. Phys., 121 (2004), pp. 11587-11598.
-
(2004)
J. Chem. Phys.
, vol.121
, pp. 11587-11598
-
-
Harrison, R.J.1
Fann, G.I.2
Yanai, T.3
Gan, Z.4
Beylkin, G.5
-
21
-
-
84861379430
-
The alternating linear scheme for tensor optimization in the tensor train format
-
S. Holtz, T. Rohwedder, and R. Schneider, The alternating linear scheme for tensor optimization in the tensor train format, SIAM J. Sci. Comput., 34 (2012), pp. A683-A713.
-
(2012)
SIAM J. Sci. Comput.
, vol.34
, pp. A683-A713
-
-
Holtz, S.1
Rohwedder, T.2
Schneider, R.3
-
22
-
-
84900564375
-
Subspace iteration methods in terms of matrix product states
-
T. Huckle and K. Waldherr, Subspace iteration methods in terms of matrix product states, PAMM Proc. Appl. Math. Mech., 12 (2012), pp. 641-642.
-
(2012)
PAMM Proc. Appl. Math. Mech.
, vol.12
, pp. 641-642
-
-
Huckle, T.1
Waldherr, K.2
-
23
-
-
84867288584
-
Low-rank explicit QTT representation of the Laplace operator and its inverse
-
V. A. Kazeev and B. N. Khoromskij, Low-rank explicit QTT representation of the Laplace operator and its inverse, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 742-758.
-
(2012)
SIAM J. Matrix Anal. Appl.
, vol.33
, pp. 742-758
-
-
Kazeev, V.A.1
Khoromskij, B.N.2
-
24
-
-
84898646167
-
Black-box Hartree-Fock solver by tensor numerical methods
-
V. Khoromskaia, Black-box Hartree-Fock solver by tensor numerical methods, Comput. Methods Appl. Math., 14 (2014), pp. 89-111.
-
(2014)
Comput. Methods Appl. Math.
, vol.14
, pp. 89-111
-
-
Khoromskaia, V.1
-
25
-
-
79952297523
-
Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format
-
B. N. Khoromskij, V. Khoromskaia, and H.-J. Flad, Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format, SIAM J. Sci. Comput., 33 (2011), pp. 45-65.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, pp. 45-65
-
-
Khoromskij, B.N.1
Khoromskaia, V.2
Flad, H.-J.3
-
26
-
-
84866509513
-
-
Technical report 69/2010, MPI MIS, Leipzig, Germany
-
B. N. Khoromskij and I. V. Oseledets, DMRG+QTT Approach to Computation of the Ground State for the Molecular Schrödinger Operator, Technical report 69/2010, MPI MIS, Leipzig, Germany, 2010.
-
(2010)
DMRG+QTT Approach to Computation of the Ground State for the Molecular Schrödinger Operator
-
-
Khoromskij, B.N.1
Oseledets, I.V.2
-
27
-
-
80053917258
-
Quantics-TT collocation approximation of parameterdependent and stochastic elliptic PDEs
-
B. N. Khoromskij and I. V. Oseledets, Quantics-TT collocation approximation of parameterdependent and stochastic elliptic PDEs, Comput. Methods Appl. Math., 10 (2010), pp. 376-394.
-
(2010)
Comput. Methods Appl. Math.
, vol.10
, pp. 376-394
-
-
Khoromskij, B.N.1
Oseledets, I.V.2
-
28
-
-
0036223489
-
Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
-
A. V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517-541.
-
(2001)
SIAM J. Sci. Comput.
, vol.23
, pp. 517-541
-
-
Knyazev, A.V.1
-
29
-
-
80053926097
-
Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems
-
D. Kressner and C. Tobler, Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems, Comput. Methods Appl. Math., 11 (2011), pp. 363-381.
-
(2011)
Comput. Methods Appl. Math.
, vol.11
, pp. 363-381
-
-
Kressner, D.1
Tobler, C.2
-
30
-
-
81355160934
-
Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format
-
O. S. Lebedeva, Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format, Russian J. Numer. Anal. Math. Modelling, 26 (2011), pp. 465-489.
-
(2011)
Russian J. Numer. Anal. Math. Modelling
, vol.26
, pp. 465-489
-
-
Lebedeva, O.S.1
-
31
-
-
0002053823
-
The multiconfigurational time-dependent Hartree approach
-
H.-D. Meyer, U. Manthe, and L.-S. Cederbaum, The multiconfigurational time-dependent Hartree approach, Chem. Phys. Lett., 165 (1990), pp. 73-78.
-
(1990)
Chem. Phys. Lett.
, vol.165
, pp. 73-78
-
-
Meyer, H.-D.1
Manthe, U.2
Cederbaum, L.-S.3
-
32
-
-
0036003403
-
A geometric theory for preconditioned inverse iteration applied to a subspace
-
K. Neymeyr, A geometric theory for preconditioned inverse iteration applied to a subspace, Math. Comp., 71 (2002), pp. 197-216.
-
(2002)
Math. Comp.
, vol.71
, pp. 197-216
-
-
Neymeyr, K.1
-
33
-
-
80053896203
-
Tensor-train decomposition
-
I. V. Oseledets, Tensor-train decomposition, SIAM J. Sci. Comput., 33 (2011), pp. 2295-2317.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, pp. 2295-2317
-
-
Oseledets, I.V.1
-
34
-
-
70449528138
-
Breaking the curse of dimensionality or how to use SVD in many dimensions
-
I. V. Oseledets and E. E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions, SIAM J. Sci. Comput., 31 (2009), pp. 3744-3759.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 3744-3759
-
-
Oseledets, I.V.1
Tyrtyshnikov, E.E.2
-
35
-
-
84856895584
-
Variational numerical renormalization group: Bridging the gap between NRG and density matrix renormalization group
-
I. Pi?zorn and F. Verstraete, Variational numerical renormalization group: Bridging the gap between NRG and density matrix renormalization group, Phys. Rev. Lett., 108 (2012), 067202.
-
(2012)
Phys. Rev. Lett.
, vol.108
, pp. 067202
-
-
Pizorn, I.1
Verstraete, F.2
-
36
-
-
0033691032
-
A numerical study on the performance of the multiconfigurational time-dependent Hartree method for density operators
-
A. Raab and H.-D. Meyer, A numerical study on the performance of the multiconfigurational time-dependent Hartree method for density operators, J. Chem. Phys., 112 (2000), pp. 10718-10729.
-
(2000)
J. Chem. Phys.
, vol.112
, pp. 10718-10729
-
-
Raab, A.1
Meyer, H.-D.2
-
37
-
-
84880562542
-
On local convergence of alternating schemes for optimization of convex problems in the tensor train format
-
T. Rohwedder and A. Uschmajew, On local convergence of alternating schemes for optimization of convex problems in the tensor train format, SIAM J. Numer. Anal., 51 (2013), pp. 1134-1162.
-
(2013)
SIAM J. Numer. Anal.
, vol.51
, pp. 1134-1162
-
-
Rohwedder, T.1
Uschmajew, A.2
-
38
-
-
0034319898
-
The trace minimization method for the symmetric generalized eigenvalue problem
-
A. H. Sameh and Z. Tong, The trace minimization method for the symmetric generalized eigenvalue problem, J. Comput. Appl. Math., 123 (2000), pp. 155-175.
-
(2000)
J. Comput. Appl. Math.
, vol.123
, pp. 155-175
-
-
Sameh, A.H.1
Tong, Z.2
-
39
-
-
0009148594
-
A trace minimization algorithm for the generalized eigenvalue problem
-
A. H. Sameh and J. A. Wisniewski, A trace minimization algorithm for the generalized eigenvalue problem, SIAM J. Numer. Anal., 19 (1982), pp. 1243-1259.
-
(1982)
SIAM J. Numer. Anal.
, vol.19
, pp. 1243-1259
-
-
Sameh, A.H.1
Wisniewski, J.A.2
-
40
-
-
78650755970
-
The density-matrix renormalization group in the age of matrix product states
-
U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Physics, 326 (2011), pp. 96-192.
-
(2011)
Ann. Physics
, vol.326
, pp. 96-192
-
-
Schollwöck, U.1
-
41
-
-
72449185787
-
Variational matrix-product-state approach to quantum impurity models
-
A. Weichselbaum, F. Verstraete, U. Schollwöck, J. I. Cirac, and J. von Delft, Variational matrix-product-state approach to quantum impurity models, Phys. Rev. B, 80 (2009), 165117.
-
(2009)
Phys. Rev. B
, vol.80
, pp. 165117
-
-
Weichselbaum, A.1
Verstraete, F.2
Schollwöck, U.3
Cirac, J.I.4
-
42
-
-
3442895828
-
Density matrix formulation for quantum renormalization groups
-
S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett., 69 (1992), pp. 2863-2866.
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 2863-2866
-
-
White, S.R.1
-
43
-
-
29644437321
-
Density matrix renormalization group algorithms with a single center site
-
S. R. White, Density matrix renormalization group algorithms with a single center site, Phys. Rev. B, 72 (2005), 180403.
-
(2005)
Phys. Rev. B
, vol.72
, pp. 180403
-
-
White, S.R.1
|