-
2
-
-
27844496824
-
Algorithms for numerical analysis in high dimensions
-
G. Beylkin and M. J. Mohlenkamp, Algorithms for numerical analysis in high dimensions. SIAM J. Sci. Comp. (2005) 26, No. 6, 2133-2159.
-
(2005)
SIAM J. Sci. Comp.
, vol.26
, Issue.6
, pp. 2133-2159
-
-
Beylki, G.1
Mohlenkamp, M.J.2
-
3
-
-
84857999258
-
A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients
-
S. Dolgov, B. N. Khoromskij, I. V. Oseledets, and E. E. Tyrtyshnikov, A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients. Linear Algebra Appl. (2011) 436, No. 9, 2980-3007.
-
(2011)
Linear Algebra Appl.
, vol.436
, Issue.9
, pp. 2980-3007
-
-
Dolgov, S.1
Khoromskij, B.N.2
Oseledets, I.V.3
Tyrtyshnikov, E.E.4
-
4
-
-
84881623467
-
Multidimensional Fourier transform in logarithmic complexity using QTT approximation
-
MPI MIS, Leipzig
-
S. V. Dolgov, B. N. Khoromskij, and D. V. Savostyanov, Multidimensional Fourier transform in logarithmic complexity using QTT approximation. Preprint No. 18. MPI MIS, Leipzig, 2011.
-
(2011)
Preprint No. 18
-
-
Dolgov, S.V.1
Khoromskij, B.N.2
Savostyanov, D.V.3
-
5
-
-
84881618151
-
Solution of linear systems and matrix inversion in the TT-format
-
MPI MIS, Leipzig
-
S. V. Dolgov and I. V. Oseledets, Solution of linear systems and matrix inversion in the TT-format. Preprint No. 19. MPI MIS, Leipzig, 2011.
-
(2011)
Preprint No. 19
-
-
Dolgo, S.V.1
Oseledets, I.V.2
-
7
-
-
77956032667
-
Hierarchical singular value decomposition of tensors
-
L. Grasedyck, Hierarchical singular value decomposition of tensors. SIAM J. Matrix Anal. Appl. (2010) 31, No. 4, 2029-2054.
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, Issue.4
, pp. 2029-2054
-
-
Grasedyck, L.1
-
8
-
-
29144513721
-
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators, I. Separable approximation of multi-variate functions
-
W. Hackbusch and B. N. Khoromskij, Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators, I. Separable approximation of multi-variate functions. Computing (2006) 76, No. 3-4. 177-202.
-
(2006)
Computing
, vol.76
, Issue.3-4
, pp. 177-202
-
-
Hackbusc, W.1
Khoromskij, B.N.2
-
9
-
-
29144481646
-
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators, II. HKT representation of certain operators
-
W. Hackbusch and B. N. Khoromskij, Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators, II. HKT representation of certain operators. Computing (2006) 76, No. 3-4. P. 203-225.
-
(2006)
Computing
, vol.76
, Issue.3-4
, pp. 203-225
-
-
Hackbusc, W.1
Khoromskij, B.N.2
-
10
-
-
77952289640
-
A new scheme for the tensor representation
-
W. Hackbusch and S. K̈uhn, A new scheme for the tensor representation. J. Fourier Anal. Appl. (2009), 15, No. 5, 706-722.
-
(2009)
J. Fourier Anal. Appl.
, vol.15
, Issue.5
, pp. 706-722
-
-
Hackbusc, W.1
K̈uhn, S.2
-
12
-
-
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. Comp. (2012) 34, No. 2, A683-A713.
-
(2012)
SIAM J. Sci. Comp.
, vol.34
, Issue.2
-
-
Holtz, S.1
Rohwedder, T.2
Schneider, R.3
-
13
-
-
84881658691
-
Explicit low-rank QTT representation of Laplace operator and its inverse
-
MPI MIS, Leipzig
-
V. Kazeev and B. N. Khoromskij, Explicit low-rank QTT representation of Laplace operator and its inverse, Preprint No. 75. MPI MIS, Leipzig, 2010.
-
(2010)
Preprint No. 75
-
-
Kazee, V.1
Khoromskij, B.N.2
-
14
-
-
79960994573
-
(D log N)-Quantics approximation of N-dtensors in highdimensional numerical modelling
-
B. N. Khoromskij, (d log N)-Quantics approximation of N-dtensors in highdimensional numerical modelling. Constr. Appr. (2011) 34, No. 2, 257-280.
-
(2011)
Constr. Appr.
, vol.34
, Issue.2
, pp. 257-280
-
-
Khoromskij, B.N.1
-
15
-
-
84866509513
-
DMRG+QTT approach to computation of the ground state for the molecular Schr̈odinger operator
-
MPI MIS, Leipzig
-
B. N. Khoromskij and I. V. Oseledets, DMRG+QTT approach to computation of the ground state for the molecular Schr̈odinger operator. Preprint No. 69. MPI MIS, Leipzig, 2010.
-
(2010)
Preprint No. 69
-
-
Khoromski, B.N.1
Oseledets, I.V.2
-
16
-
-
80053917258
-
Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs
-
B. N. Khoromskij and I. V. Oseledets, Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Comput. Meth. Appl. Math. (2010) 10, No. 4, 376-394.
-
(2010)
Comput. Meth. Appl. Math.
, vol.10
, Issue.4
, pp. 376-394
-
-
Khoromski, B.N.1
Oseledets, I.V.2
-
17
-
-
68649096448
-
Tensor decompositions and applications
-
T. G. Kolda and B. W. Bader, Tensor decompositions and applications. SIAM Review (2009) 51, No. 3, 455-500.
-
(2009)
SIAM Review
, vol.51
, Issue.3
, pp. 455-500
-
-
Kold, T.G.1
Bader, B.W.2
-
18
-
-
77956045829
-
Krylov subspace methods for linear systems with tensor product structure
-
D. Kressner and C. Tobler, Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl. (2010) 31, 1688-1714.
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 1688-1714
-
-
Kressne, D.1
Tobler, C.2
-
19
-
-
79956161187
-
Low-rank tensor Krylov subspace methods for parametrized linear systems
-
Seminar for applied mathematics, ETH Zurich
-
D. Kressner and C. Tobler, Low-rank tensor Krylov subspace methods for parametrized linear systems. Research report. Seminar for applied mathematics, ETH Zurich, 2010.
-
(2010)
Research Report
-
-
Kressne, D.1
Tobler, C.2
-
20
-
-
77952874303
-
Block tensor conjugate gradient-type method for Rayleigh quotient minimization in two-dimensional case
-
O. S. Lebedeva, Block tensor conjugate gradient-type method for Rayleigh quotient minimization in two-dimensional case. Comp. Math. Math. Phys. (2010) 50, No. 5, 749-765.
-
(2010)
Comp. Math. Math. Phys.
, vol.50
, Issue.5
, pp. 749-765
-
-
Lebedeva, O.S.1
-
23
-
-
77953297072
-
Compact matrix form of the d-dimensional tensor decomposition
-
INM RAS, Moscow
-
I. V. Oseledets, Compact matrix form of the d-dimensional tensor decomposition. Preprint No. 2009-01. INM RAS, Moscow, 2009.
-
(2009)
Preprint No. 2009-01
-
-
Oseledets, I.V.1
-
24
-
-
77956042755
-
d matrices using tensor decomposition
-
d matrices using tensor decomposition. SIAM J. Matrix Anal. Appl. (2010) 31, No. 4, 2130-2145.
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, Issue.4
, pp. 2130-2145
-
-
Oseledets, I.V.1
-
25
-
-
80053929473
-
DMRG approach to fast linear algebra in the TT-format
-
I. V. Oseledets, DMRG approach to fast linear algebra in the TT-format. Comput. Meth. Appl. Math. (2011) 11, No. 3, 382-393.
-
(2011)
Comput. Meth. Appl. Math
, vol.11
, Issue.3
, pp. 382-393
-
-
Oseledets, I.V.1
-
26
-
-
80053896203
-
Tensor-train decomposition
-
I. V. Oseledets, Tensor-train decomposition. SIAM J. Sci. Comput. (2011) 33, No. 5, 2295-2317.
-
(2011)
SIAM J. Sci. Comput.
, vol.33
, Issue.5
, pp. 2295-2317
-
-
Oseledets, I.V.1
-
27
-
-
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. (2009) 31, No. 5, 3744-3759.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, Issue.5
, pp. 3744-3759
-
-
Oseledet, I.V.1
Tyrtyshnikov, E.E.2
-
28
-
-
0000048673
-
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
-
Y. Saad and M. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. (1986) 7, No. 3, 856-869.
-
(1986)
SIAM J. Sci. Stat. Comput.
, vol.7
, Issue.3
, pp. 856-869
-
-
Saa, Y.1
Schultz, M.2
-
29
-
-
2342652956
-
Theory of inexact Krylov subspace methods and applications to scientific computing
-
V. Simoncini and D. B. Szyld, Theory of inexact Krylov subspace methods and applications to scientific computing. SIAM J. Sci. Comput. (2003) 25, 454-477.
-
(2003)
SIAM J. Sci. Comput.
, vol.25
, pp. 454-477
-
-
Simoncin, V.1
Szyld, D.B.2
-
30
-
-
0002522806
-
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals
-
I. Sloan and H. Wozniakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals. J. Complexity (1998) 14, No. 1, 1-33.
-
(1998)
J. Complexity
, vol.14
, Issue.1
, pp. 1-33
-
-
Sloa, I.1
Wozniakowski, H.2
-
31
-
-
3042570112
-
A unifying approach to some old and new theorems on distribution and clustering
-
E. E. Tyrtyshnikov, A unifying approach to some old and new theorems on distribution and clustering. Linear Algebra Appl. (1996), No. 323, 1-43.
-
(1996)
Linear Algebra Appl.
, vol.323
, pp. 1-43
-
-
Tyrtyshnikov, E.E.1
-
32
-
-
13844311486
-
Inexact Krylov subspace methods for linear systems
-
J. van den Eshof and G. L. G. Sleijpen, Inexact Krylov subspace methods for linear systems. SIAM J. Matrix Anal. Appl. (2004) 26, No. 1, 125-153.
-
(2004)
SIAM J. Matrix Anal. Appl.
, vol.26
, Issue.1
, pp. 125-153
-
-
Van Den Esho, J.1
Sleijpen, G.L.G.2
-
33
-
-
33144490090
-
Why are high-dimensional finance problems often of low effective dimension?
-
X. Wang and I. H. Sloan, Why are high-dimensional finance problems often of low effective dimension? SIAM J. Sci. Comp. (2006) 27, No. 1, 159-183.
-
(2006)
SIAM J. Sci. Comp.
, vol.27
, Issue.1
, pp. 159-183
-
-
Wan, X.1
Sloan, I.H.2
|