-
1
-
-
33751260933
-
A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids
-
A. Ammar, B. Mokdad, F. Chinesta and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J. Non-Newtonian Fluid Mech. 139 (2006) 153-176.
-
(2006)
J. Non-Newtonian Fluid Mech.
, vol.139
, pp. 153-176
-
-
Ammar, A.1
Mokdad, B.2
Chinesta, F.3
Keunings, R.4
-
2
-
-
78549238137
-
On the convergence of a greedy rank-one update algorithm for a class of linear systems
-
A. Ammar, F. Chinesta and A. Falco, On the convergence of a greedy rank-one update algorithm for a class of linear systems. Arch. Comput. Methods Engrg. 17 (2010) 473-486.
-
(2010)
Arch. Comput. Methods Engrg.
, vol.17
, pp. 473-486
-
-
Ammar, A.1
Chinesta, F.2
Falco, A.3
-
3
-
-
84938959813
-
Adaptive near-optimal rank tensor approximation for high-dimensional operator equations
-
M. Bachmayr and W. Dahmen, Adaptive near-optimal rank tensor approximation for high-dimensional operator equations. Found. Comput. Math. (2014) DOI:10.1007/s10208-013-9187-3.
-
(2014)
Found. Comput. Math.
-
-
Bachmayr, M.1
Dahmen, W.2
-
4
-
-
84870908752
-
A projection method to solve linear systems in tensor format
-
J. Ballani and L. Grasedyck, A projection method to solve linear systems in tensor format. Numer. Linear Algebra Appl. 20 (2013) 27-43.
-
(2013)
Numer. Linear Algebra Appl.
, vol.20
, pp. 27-43
-
-
Ballani, J.1
Grasedyck, L.2
-
5
-
-
27844496824
-
Algorithms for numerical analysis in high dimensions
-
G. Beylkin and M.J. Mohlenkamp, Algorithms for numerical analysis in high dimensions. SIAM J. Sci. Comput. 26 (2005) 2133-2159.
-
(2005)
SIAM J. Sci. Comput.
, vol.26
, pp. 2133-2159
-
-
Beylkin, G.1
Mohlenkamp, M.J.2
-
6
-
-
80255141549
-
Convergence of a greedy algorithm for high-dimensional convex nonlinear problems
-
E. Cances, V. Ehrlacher and T. Lelievre, Convergence of a greedy algorithm for high-dimensional convex nonlinear problems. Math. Models Methods Appl. Sci. 21 (2011) 2433-2467.
-
(2011)
Math. Models Methods Appl. Sci.
, vol.21
, pp. 2433-2467
-
-
Cances, E.1
Ehrlacher, V.2
Lelievre, T.3
-
8
-
-
84861889869
-
Adaptivity and variational stabilization for convection-diffusion equations
-
A. Cohen, W. Dahmen and G. Welper, Adaptivity and variational stabilization for convection-diffusion equations. ESAIM: M2AN 46 (2012) 1247-1273.
-
(2012)
ESAIM: M2AN
, vol.46
, pp. 1247-1273
-
-
Cohen, A.1
Dahmen, W.2
Welper, G.3
-
9
-
-
80255135543
-
A short review on model order reduction based on proper generalized decomposition
-
F. Chinesta, P. Ladeveze and E. Cueto, A short review on model order reduction based on proper generalized decomposition. Arch. Comput. Methods Engrg. 18 (2011) 395-404.
-
(2011)
Arch. Comput. Methods Engrg.
, vol.18
, pp. 395-404
-
-
Chinesta, F.1
Ladeveze, P.2
Cueto, E.3
-
10
-
-
84868375667
-
Adaptive petrov-galerkin methods for first order transport equations
-
W. Dahmen, C. Huang, C. Schwab and G. Welper, Adaptive petrov-galerkin methods for first order transport equations. SIAM J. Numer. Anal. 50 (2012) 2420-2445.
-
(2012)
SIAM J. Numer. Anal.
, vol.50
, pp. 2420-2445
-
-
Dahmen, W.1
Huang, C.2
Schwab, C.3
Welper, G.4
-
12
-
-
67349208768
-
A least-squares approximation of partial differential equations with high-dimensional random inputs
-
A. Doostan and G. Iaccarino, A least-squares approximation of partial differential equations with high-dimensional random inputs. J. Comput. Phys. 228 (2009) 4332-4345.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 4332-4345
-
-
Doostan, A.1
Iaccarino, G.2
-
13
-
-
11244324581
-
Theory and practice of finite elements
-
A. Ern and J.-L. Guermond, Theory and practice of finite elements. Vol. 159 of Appl. Math. Sci. (2004).
-
(2004)
Appl. Math. Sci.
, vol.159
-
-
Ern, A.1
Guermond, J.-L.2
-
14
-
-
84867520186
-
A regularized newton method for the efficient approximation of tensors represented in the canonical tensor format
-
M. Espig and W. Hackbusch, A regularized newton method for the efficient approximation of tensors represented in the canonical tensor format. Numer. Math. 122 (2012) 489-525.
-
(2012)
Numer. Math.
, vol.122
, pp. 489-525
-
-
Espig, M.1
Hackbusch, W.2
-
15
-
-
78650698308
-
A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach
-
A. Falcó and A. Nouy, A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach. J. Math. Anal. Appl. 376 (2011) 469-480.
-
(2011)
J. Math. Anal. Appl.
, vol.376
, pp. 469-480
-
-
Falcó, A.1
Nouy, A.2
-
16
-
-
84868196670
-
On minimal subspaces in tensor representations
-
A. Falcó and W. Hackbusch, On minimal subspaces in tensor representations. Found. Comput. Math. 12 (2012) 765-803.
-
(2012)
Found. Comput. Math.
, vol.12
, pp. 765-803
-
-
Falcó, A.1
Hackbusch, W.2
-
17
-
-
84862262704
-
Proper generalized decomposition for nonlinear convex problems in tensor banach spaces
-
A. Falcó and A. Nouy, Proper generalized decomposition for nonlinear convex problems in tensor banach spaces. Numer. Math. 121 (2012) 503-530.
-
(2012)
Numer. Math.
, vol.121
, pp. 503-530
-
-
Falcó, A.1
Nouy, A.2
-
19
-
-
84866540803
-
Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators
-
L. Figueroa and E. Suli, Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators. Found. Comput. Math. 12 (2012) 573-623.
-
(2012)
Found. Comput. Math.
, vol.12
, pp. 573-623
-
-
Figueroa, L.1
Suli, E.2
-
22
-
-
77956032667
-
Hierarchical singular value decomposition of tensors
-
L. Grasedyck, Hierarchical singular value decomposition of tensors. SIAM J. Matrix Anal. Appl. 31 (2010) 2029-2054.
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 2029-2054
-
-
Grasedyck, L.1
-
23
-
-
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-Mitteilungen 36 (2013) 53-78.
-
(2013)
GAMM-Mitteilungen
, vol.36
, pp. 53-78
-
-
Grasedyck, L.1
Kressner, D.2
Tobler, C.3
-
25
-
-
77952289640
-
A New Scheme for the Tensor Representation
-
W. Hackbusch and S. Kuhn, A New Scheme for the Tensor Representation. J. Fourier Anal. Appl. 15 (2009) 706-722.
-
(2009)
J. Fourier Anal. Appl.
, vol.15
, pp. 706-722
-
-
Hackbusch, W.1
Kuhn, S.2
-
26
-
-
84861379430
-
The Alternating Linear Scheme for Tensor Optimisation in the TT format
-
S. Holtz, T. Rohwedder and R. Schneider, The Alternating Linear Scheme for Tensor Optimisation in the TT format. SIAM J. Sci. Comput. 34 (2012) 683-713.
-
(2012)
SIAM J. Sci. Comput.
, vol.34
, pp. 683-713
-
-
Holtz, S.1
Rohwedder, T.2
Schneider, R.3
-
27
-
-
84858291641
-
On manifolds of tensors with fixed TT rank
-
S. Holtz, T. Rohwedder and R. Schneider, On manifolds of tensors with fixed TT rank. Numer. Math. 120 (2012) 701-731.
-
(2012)
Numer. Math.
, vol.120
, pp. 701-731
-
-
Holtz, S.1
Rohwedder, T.2
Schneider, R.3
-
28
-
-
79952300361
-
Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs
-
B.N. Khoromskij and C. Schwab, Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. SIAM J. Sci. Comput. 33 (2011) 364-385.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, pp. 364-385
-
-
Khoromskij, B.N.1
Schwab, C.2
-
29
-
-
83655192088
-
Tensors-structured numerical methods in scientific computing: Survey on recent advances
-
B.N. Khoromskij, Tensors-structured numerical methods in scientific computing: Survey on recent advances. Chemometrics and Intelligent Laboratory Systems 110 (2012) 1-19.
-
(2012)
Chemometrics and Intelligent Laboratory Systems
, vol.110
, pp. 1-19
-
-
Khoromskij, B.N.1
-
30
-
-
68649096448
-
Tensor decompositions and applications
-
T.G. Kolda and B.W. Bader, Tensor decompositions and applications. SIAM Review 51 (2009) 455-500.
-
(2009)
SIAM Review
, vol.51
, pp. 455-500
-
-
Kolda, T.G.1
Bader, B.W.2
-
31
-
-
84856290662
-
Low-rank tensor krylov subspace methods for parametrized linear systems
-
D. Kressner and C. Tobler, Low-rank tensor krylov subspace methods for parametrized linear systems. SIAM J. Matrix Anal. Appl. 32 (2011) 1288-1316.
-
(2011)
SIAM J. Matrix Anal. Appl.
, vol.32
, pp. 1288-1316
-
-
Kressner, D.1
Tobler, C.2
-
33
-
-
76549123073
-
The LATIN multiscale computational method and the Proper Generalized Decomposition
-
P. Ladevèze, J.C. Passieux and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1287-1296.
-
(2010)
Comput. Methods Appl. Mech. Engrg.
, vol.199
, pp. 1287-1296
-
-
Ladevèze, P.1
Passieux, J.C.2
Néron, D.3
-
34
-
-
84858793640
-
Solving stochastic systems with low-rank tensor compression
-
H. G. Matthies and E. Zander, Solving stochastic systems with low-rank tensor compression. Linear Algebra Appl. 436 (2012).
-
(2012)
Linear Algebra Appl.
, vol.436
-
-
Matthies, H.G.1
Zander, E.2
-
35
-
-
34548290926
-
A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
-
A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Comput. Methods Appl. Mech. Engrg. 196 (2007) 4521-4537.
-
(2007)
Comput. Methods Appl. Mech. Engrg.
, vol.196
, pp. 4521-4537
-
-
Nouy, A.1
-
36
-
-
71349087893
-
Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations
-
A. Nouy, Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations, Arch. Comput. Methods Engrg. 16 (2009) 251-285.
-
(2009)
Arch. Comput. Methods Engrg.
, vol.16
, pp. 251-285
-
-
Nouy, A.1
-
37
-
-
78549263686
-
Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems
-
A. Nouy, Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems. Arch. Comput. Methods Engrg. 17 (2010) 403-434.
-
(2010)
Arch. Comput. Methods Engrg.
, vol.17
, pp. 403-434
-
-
Nouy, A.1
-
38
-
-
77951238456
-
A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
-
A. Nouy, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1603-1626.
-
(2010)
Comput. Methods Appl. Mech. Engrg.
, vol.199
, pp. 1603-1626
-
-
Nouy, A.1
-
39
-
-
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) 3744-3759.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 3744-3759
-
-
Oseledets, I.V.1
Tyrtyshnikov, E.E.2
-
40
-
-
80053896203
-
Tensor-train decomposition
-
I.V. Oseledets, Tensor-train decomposition. SIAM J. Sci. Comput. 33 (2011) 2295-2317.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, pp. 2295-2317
-
-
Oseledets, I.V.1
-
41
-
-
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) 1134-1162.
-
(2013)
SIAM J. Numer. Anal.
, vol.51
, pp. 1134-1162
-
-
Rohwedder, T.1
Uschmajew, A.2
-
43
-
-
58149380535
-
Greedy approximation
-
V. Temlyakov, Greedy approximation. Acta Numerica 17 (2008) 235-409.
-
(2008)
Acta Numerica
, vol.17
, pp. 235-409
-
-
Temlyakov, V.1
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