-
1
-
-
77954348131
-
A stochastic collocation method for elliptic partial differential equations with random input data
-
I. Babuška, F. Nobile, and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM Rev., 52 (2010), pp. 317-355.
-
(2010)
SIAM Rev.
, vol.52
, pp. 317-355
-
-
Babuška, I.1
Nobile, F.2
Tempone, R.3
-
2
-
-
0036679114
-
Numerical operator calculus in higher dimensions
-
G. Beylkin and M. M. Mohlenkamp, Numerical operator calculus in higher dimensions, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 10246-10251.
-
(2002)
Proc. Natl. Acad. Sci. USA
, vol.99
, pp. 10246-10251
-
-
Beylkin, G.1
Mohlenkamp, M.M.2
-
3
-
-
27844496824
-
Algorithms for numerical analysis in high dimensions
-
DOI 10.1137/040604959
-
G. Beylkin and M. J. Mohlenkamp, Algorithms for numerical analysis in high dimensions, SIAM J. Sci. Comput., 26 (2005), pp. 2133-2159. (Pubitemid 41641365)
-
(2005)
SIAM Journal of Scientific Computing
, vol.26
, Issue.6
, pp. 2133-2159
-
-
Beylkin, G.1
Mohlenkamp, M.J.2
-
4
-
-
78651581790
-
Sparse tensor discretization of elliptic sPDEs
-
M. Bieri, R. Andreev, and Ch. Schwab, Sparse tensor discretization of elliptic sPDEs, SIAM J. Sci. Comput., 31 (2009), pp. 4281-4304.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 4281-4304
-
-
Bieri, M.1
Andreev, R.2
Schwab, C.3
-
7
-
-
77957936449
-
Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs
-
A. Cohen, R. DeVore, and Ch. Schwab, Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs, Found. Comput. Math., 10 (2010), pp. 615-646.
-
(2010)
Found. Comput. Math.
, vol.10
, pp. 615-646
-
-
Cohen, A.1
DeVore, R.2
Schwab, C.3
-
9
-
-
0034144758
-
A Multilinear Singular Value Decomposition
-
DOI 10.1137/S0895479896305696
-
L. De Lathauwer, B. De Moor, and J. Vandewalle, A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1253-1278. (Pubitemid 33217068)
-
(2000)
SIAM Journal on Matrix Analysis and Applications
, vol.21
, Issue.4
, pp. 1253-1278
-
-
De Lathauwer, L.1
De Moor, B.2
Vandewalle, J.3
-
10
-
-
10444261986
-
Finite elements for elliptic problems with stochastic coefficients
-
DOI 10.1016/j.cma.2004.04.008, PII S0045782504003299
-
Ph. Frauenfelder, Ch. Schwab, and R.-A. Todor, Finite elements for elliptic problems with stochastic coefficients, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 205-228. (Pubitemid 39637479)
-
(2005)
Computer Methods in Applied Mechanics and Engineering
, vol.194
, pp. 205-228
-
-
Frauenfelder, P.1
Schwab, C.2
Todor, R.A.3
-
11
-
-
17144410769
-
Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
-
DOI 10.1007/s00607-004-0086-y
-
I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions, Computing, 74 (2005), pp. 131-157. (Pubitemid 40512277)
-
(2005)
Computing (Vienna/New York)
, vol.74
, Issue.2
, pp. 131-157
-
-
Gavrilyuk, I.P.1
Hackbusch, W.2
Khoromskij, B.N.3
-
12
-
-
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
-
14
-
-
29144513721
-
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multi-variate functions
-
DOI 10.1007/s00607-005-0144-0
-
W. Hackbusch and B. N. Khoromskij, Low-rank Kronecker product approximation to multidimensional nonlocal operators. Part I. Separable approximation of multi-variate functions, Computing, 76 (2006), pp. 177-202. (Pubitemid 41813085)
-
(2006)
Computing (Vienna/New York)
, vol.76
, Issue.3-4
, pp. 177-202
-
-
Hackbusch, W.1
Khoromskij, B.N.2
-
15
-
-
77951823247
-
-
Preprint 78, MPIMiS, Leipzig, Germany, submitted
-
W. Hackbusch, B.N. Khoromskij, S. Sauter, and E. Tyrtyshnikov, Use of Tensor Formats in Elliptic Eigenvalue Problems, Preprint 78, MPIMiS, Leipzig, Germany, 2008, submitted.
-
(2008)
Use of Tensor Formats in Elliptic Eigenvalue Problems
-
-
Hackbusch, W.1
Khoromskij, B.N.2
Sauter, S.3
Tyrtyshnikov, E.4
-
16
-
-
21244436795
-
Hierarchical Kronecker tensorproduct approximations
-
W. Hackbusch, B. N. Khoromskij, and E. E. Tyrtyshnikov, Hierarchical Kronecker tensorproduct approximations, J. Numer. Math., 13 (2005), pp. 119-156.
-
(2005)
J. Numer. Math.
, vol.13
, pp. 119-156
-
-
Hackbusch, W.1
Khoromskij, B.N.2
Tyrtyshnikov, E.E.3
-
17
-
-
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
-
19
-
-
47849118953
-
On tensor approximation of Green iterations for Kohn-Sham equations
-
B. N. Khoromskij, On tensor approximation of Green iterations for Kohn-Sham equations, Comput. Vis. Sci., 11 (2008), pp. 259-271.
-
(2008)
Comput. Vis. Sci.
, vol.11
, pp. 259-271
-
-
Khoromskij, B.N.1
-
21
-
-
79960994573
-
O(d logN)-quantics approximation of N-d tensors in high-dimensional numerical modeling
-
to appear
-
B. N. Khoromskij, O(d logN)-quantics approximation of N-d tensors in high-dimensional numerical modeling, Constr. Approx., 2011, to appear.
-
(2011)
Constr. Approx.
-
-
Khoromskij, B.N.1
-
22
-
-
79952291046
-
-
Preprint 21/2010, MPI MiS, Leipzig, Germany, submitted
-
B. N. Khoromskij, Tensor-Structured Numerical Methods in Scientific Computing: Survey on Recent Advances, Preprint 21/2010, MPI MiS, Leipzig, Germany, 2010, submitted.
-
(2010)
Tensor-Structured Numerical Methods in Scientific Computing: Survey on Recent Advances
-
-
Khoromskij, B.N.1
-
23
-
-
84897586218
-
Multigrid accelerated tensor approximation of function related multidimensional arrays
-
B. N. Khoromskij and V. Khoromskaia, Multigrid accelerated tensor approximation of function related multidimensional arrays, SIAM J. Sci. Comput., 31 (2009), pp. 3002-3026.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 3002-3026
-
-
Khoromskij, B.N.1
Khoromskaia, V.2
-
24
-
-
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
-
25
-
-
80053917258
-
Quantics-TT collocation approximation of parameterdependent and stochastic elliptic PDEs
-
B. N. Khoromskij and I. Oseledets, Quantics-TT collocation approximation of parameterdependent and stochastic elliptic PDEs, Comput. Methods Appl. Math., 10 (2010), pp. 345-365.
-
(2010)
Comput. Methods Appl. Math.
, vol.10
, pp. 345-365
-
-
Khoromskij, B.N.1
Oseledets, I.2
-
26
-
-
68649096448
-
Tensor decompositions and applications
-
T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev., 51 (2009), pp. 455-500.
-
(2009)
SIAM Rev.
, vol.51
, pp. 455-500
-
-
Kolda, T.G.1
Bader, B.W.2
-
28
-
-
51849118006
-
Tucker dimensionality reduction of three-dimensional arrays in linear time
-
I. V. Oseledets, D. V. Savostianov, and E. E. Tyrtyshnikov, Tucker dimensionality reduction of three-dimensional arrays in linear time, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 939-956.
-
(2008)
SIAM J. Matrix Anal. Appl.
, vol.30
, pp. 939-956
-
-
Oseledets, I.V.1
Savostianov, D.V.2
Tyrtyshnikov, E.E.3
-
29
-
-
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
-
30
-
-
0343786212
-
-
Academic Press, New York, London
-
M. Reed and B. Simon, Methods of Modern Mathematical Physics, I. Functional Analysis, Academic Press, New York, London, 1972.
-
(1972)
Methods of Modern Mathematical Physics, I. Functional Analysis
-
-
Reed, M.1
Simon, B.2
-
32
-
-
0242370956
-
Sparse finite elements for elliptic problems with stochastic loading
-
C. Schwab and R.-A. Todor, Sparse finite elements for elliptic problems with stochastic loading, Numer. Math., 95 (2003), pp. 707-713.
-
(2003)
Numer. Math.
, vol.95
, pp. 707-713
-
-
Schwab, C.1
Todor, R.-A.2
-
33
-
-
33746346426
-
Karhunen-Loève approximation of random fields by generalized fast multipole methods
-
DOI 10.1016/j.jcp.2006.01.048, PII S0021999106000349
-
C. Schwab and R.-A. Todor, Karhunen-Loève approximation of random fields by generalized fast multipole methods, J. Comput. Phys., 217 (2006), pp. 100-122. (Pubitemid 44111671)
-
(2006)
Journal of Computational Physics
, vol.217
, Issue.1
, pp. 100-122
-
-
Schwab, C.1
Todor, R.A.2
-
34
-
-
19344375707
-
-
Wiley, Chichester, UK
-
A. Smilde, R. Bro, and P. Geladi, Multiway Analysis, Wiley, Chichester, UK, 2004.
-
(2004)
Multiway Analysis
-
-
Smilde, A.1
Bro, R.2
Geladi, P.3
-
35
-
-
34047123580
-
Convergence rate for sparse chaos approximations of elliptic problems with stochastic coefficients
-
R.-A. Todor and Ch. Schwab, Convergence rate for sparse chaos approximations of elliptic problems with stochastic coefficients, IMA J. Numer. Anal., 27 (2007), pp. 232-261.
-
(2007)
IMA J. Numer. Anal.
, vol.27
, pp. 232-261
-
-
Todor, R.-A.1
Schwab, C.2
-
36
-
-
0013953617
-
Some mathematical notes on three-mode factor analysis
-
L. R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika, 31 (1966), pp. 279-311.
-
(1966)
Psychometrika
, vol.31
, pp. 279-311
-
-
Tucker, L.R.1
|