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Hackbusch, Wolfgang

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Author ID: hackbusch.wolfgang Recent zbMATH articles by "Hackbusch, Wolfgang"
Published as: Hackbusch, Wolfgang; Hackbusch, W.
Homepage: https://www.mis.mpg.de/scicomp/hackbusch.de.html
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Co-Authors

101 single-authored
23 Khoromskiĭ, Boris Nikolaevich
21 Sauter, Stefan A.
14 Grasedyck, Lars
12 Wittum, Gabriel
8 Börm, Steffen
8 Espig, Mike
7 Schneider, Reinhold
6 Flad, Heinz-Jürgen
6 Graham, Ivan G.
6 Trottenberg, Ulrich
5 Braess, Dietrich
5 Gavrilyuk, Ivan P.
4 Bank, Randolph E.
4 Kriemann, Ronald
3 Bebendorf, Mario
3 Falcó, Antonio
3 Kress, Wendy
3 Reusken, Arnold
3 Tyrtyshnikov, Evgeniĭ Evgen’evich
3 Uschmajew, André
2 Chinnamsetty, Sambasiva Rao
2 Dahmen, Wolfgang A.
2 Dryja, Maksymilian
2 Kolb, Dietmar
2 Le Borne, Sabine
2 Litvinenko, Alexander
2 Luo, Hongjun
2 Matthies, Hermann Georg
2 Nouy, Anthony
2 Nowak, Zenon P.
2 Probst, Thomas
2 Schwab, Christoph
2 Wolters, Carsten H.
1 Ballmann, Josef
1 Banjai, Lehel
1 Bastian, Peter
1 Burmeister, Jens
1 Busch, W.
1 Carstensen, Carsten
1 Chipot, Michel
1 Dahlke, Stephan
1 Dittrich, Susanne
1 Eppler, Richard
1 Faermann, Birgit
1 Funken, Stefan A.
1 Gittel, Hans-Peter
1 Greff, Isabelle
1 Griebel, Michael
1 Grosche, Günter
1 Grosse, Harald
1 Hagemann, Sigrid
1 Handschuh, Stefan
1 Härdtlein, J.
1 Herrmann, Ulrich
1 Hoàng Xuân Phù
1 Hofmann, Götz
1 Hoppe, Ronald H. W.
1 John, Volker
1 Khachatryan, Aram
1 Knödel, Walter
1 Köstler, Harald
1 Kressner, Daniel
1 Löhndorf, Maike
1 Maitre, Jean-François
1 Miranker, Willard Lee
1 Mittelmann, Hans Detlef
1 Monk, Peter B.
1 Naraparaju, Kishore Kumar
1 Nielsen, Bjørn Fredrik
1 Novak, Z. P.
1 Rannacher, Rolf
1 Ritter, Klaus
1 Rohwedder, Thorsten
1 Schneider, Jan
1 Schwarz, Hans Rudolf
1 Stetter, Hans J.
1 Suciu, Carina
1 Tveito, Aslak
1 Veit, Alexander
1 Wähnert, Philipp
1 Wappler, J. U.
1 Will, Th.
1 Witsch, Kristian
1 Yserentant, Harry
1 Zander, Elmar K.
1 Zeidler, Eberhard
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Serials

29 Computing
25 Numerische Mathematik
8 Springer Series in Computational Mathematics
6 IMA Journal of Numerical Analysis
6 Vietnam Journal of Mathematics
5 Computing and Visualization in Science
5 Oberwolfach Reports
4 Mathematics of Computation
4 SIAM Journal on Numerical Analysis
4 Numerical Linear Algebra with Applications
3 Journal of Numerical Mathematics
3 Leitfäden der Angewandten Mathematik und Mechanik (LAMM)
3 Lecture Notes in Computational Science and Engineering
3 PAMM. Proceedings in Applied Mathematics and Mechanics
2 Journal of Computational Physics
2 Arkiv för Matematik
2 Applied Numerical Mathematics
2 SIAM Journal on Matrix Analysis and Applications
2 Foundations of Computational Mathematics
2 Computational Methods in Applied Mathematics
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Applied Mathematical Sciences
2 ISNM. International Series of Numerical Mathematics
2 Lecture Notes in Mathematics
2 S\(\vec{\text{e}}\)MA Journal
2 Beiträge zur Numerischen Mathematik
1 Computers & Mathematics with Applications
1 International Journal for Numerical Methods in Fluids
1 Inverse Problems
1 Journal of the Institute of Mathematics and its Applications
1 Revue Roumaine de Mathématiques Pures et Appliquées
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
1 Aplikace Matematiky
1 Archivum Mathematicum
1 BIT
1 Control and Cybernetics
1 Journal of Computational and Applied Mathematics
1 Journal of Optimization Theory and Applications
1 Rostocker Mathematisches Kolloquium
1 SIAM Journal on Control and Optimization
1 Rendiconti del Seminario Matematico
1 SIAM Journal on Scientific and Statistical Computing
1 Zeitschrift für Analysis und ihre Anwendungen
1 Journal of Complexity
1 Constructive Approximation
1 Mathematica Bohemica
1 Applications of Mathematics
1 Linear Algebra and its Applications
1 Praxis der Mathematik
1 SIAM Journal on Scientific Computing
1 Vychislitel’nye Protsessy i Sistemy
1 East-West Journal of Numerical Mathematics
1 Engineering Analysis with Boundary Elements
1 The Journal of Fourier Analysis and Applications
1 Documenta Mathematica
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Matematicheskoe Modelirovanie
1 Acta Numerica
1 Wissenschaftliche Beiträge der Ingenieurhochschule Wismar
1 SIAM Journal on Applied Algebra and Geometry

Publications by Year

Citations contained in zbMATH Open

182 Publications have been cited 4,449 times in 2,651 Documents Cited by Year
Multi-grid methods and applications. Zbl 0595.65106
Hackbusch, Wolfgang
391
1985
A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices. Zbl 0927.65063
Hackbusch, W.
293
1999
Tensor spaces and numerical tensor calculus. Zbl 1244.65061
Hackbusch, Wolfgang
218
2012
Multi-grid eigenvalue computation. Zbl 0585.65030
Hackbusch, W.
184
1985
On the fast matrix multiplication in the boundary element method by panel clustering. Zbl 0641.65038
Hackbusch, W.; Nowak, Z. P.
173
1989
Construction and arithmetics of \(\mathcal H\)-matrices. Zbl 1030.65033
Grasedyck, Lars; Hackbusch, Wolfgang
126
2003
A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems. Zbl 0962.65029
Hackbusch, W.; Khoromskij, B. N.
121
2000
A new scheme for the tensor representation. Zbl 1188.15022
Hackbusch, W.; Kühn, S.
118
2009
Multigrid methods of the second kind. Zbl 0577.65118
Hackbusch, W.
117
1985
Integral equations. Theory and numerical treatment. Zbl 0823.65139
Hackbusch, Wolfgang
113
1995
Introduction to hierarchical matrices with applications. Zbl 1035.65042
Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang
98
2003
Hierarchical matrices: algorithms and analysis. Zbl 1336.65041
Hackbusch, Wolfgang
97
2015
On first and second order box schemes. Zbl 0649.65052
Hackbusch, Wolfgang
97
1989
A new convergence proof for the multigrid method including the V-cycle. Zbl 0521.65079
Braess, Dietrich; Hackbusch, Wolfgang
77
1983
Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients. Zbl 1033.65100
Bebendorf, Mario; Hackbusch, Wolfgang
75
2003
Iterative solution of large sparse systems of equations. Transl. from the German. Zbl 0789.65017
Hackbusch, Wolfgang
70
1994
Elliptic differential equations: theory and numerical treatment. Transl. from the German by Regine Fadiman and Patrick D. F. Ion. Zbl 0755.35021
Hackbusch, Wolfgang
65
1992
Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices. Zbl 1012.65023
Hackbusch, W.; Börm, S.
60
2002
On \({\mathcal H}^2\)-matrices. Zbl 0963.65043
Hackbusch, W.; Khoromskij, B.; Sauter, S. A.
53
2000
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions. Zbl 1087.65049
Hackbusch, W.; Khoromskij, B. N.
51
2006
Theorie und Numerik elliptischer Differentialgleichungen. Zbl 0609.65065
Hackbusch, Wolfgang
50
1986
Composite finite elements for the approximation of PDEs on domains with complicated micro-structures. Zbl 0874.65086
Hackbusch, W.; Sauter, S. A.
47
1997
Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Zbl 1239.65026
Grasedyck, Lars; Hackbusch, Wolfgang; Khoromskij, B. N.
43
2003
Approximation of \(1/x\) by exponential sums in \([1, \infty]\). Zbl 1082.65025
Braess, Dietrich; Hackbusch, Wolfgang
42
2005
Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
41
2005
A numerical method for solving parabolic equations with opposite orientations. Zbl 0391.65044
Hackbusch, W.
40
1978
Approximate iterations for structured matrices. Zbl 1144.65029
Hackbusch, Wolfgang; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E.
40
2008
Hierarchical matrices. Algorithms and analysis. (Hierarchische Matrizen. Algorithmen und Analysis.) Zbl 1180.65004
Hackbusch, Wolfgang
40
2009
\(\mathcal H^2\)-matrix approximation of integral operators by interpolation. Zbl 1019.65103
Hackbusch, Wolfgang; Börm, Steffen
39
2002
Hierarchical Kronecker tensor-product approximations. Zbl 1081.65035
Hackbusch, W.; Khoromskij, B. N.; Tyrtyshnikov, E. E.
39
2005
Hierarchical matrices based on a weak admissibility criterion. Zbl 1063.65035
Hackbusch, W.; Khoromskij, B. N.; Kriemann, R.
36
2004
Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
36
2005
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110
Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A.
34
2004
On the efficient computation of high-dimensional integrals and the approximation by exponential sums. Zbl 1190.65036
Braess, Dietrich; Hackbusch, Wolfgang
31
2009
Elliptic differential equations: theory and numerical treatment. Transl. from the German by Regine Fadiman and Patrick D. F. Ion. Paperback reprint of 1992 hardback edition. Zbl 1205.35060
Hackbusch, Wolfgang
30
2010
A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates. Zbl 0977.65036
Hackbusch, W.; Khoromskij, B. N.
29
2000
Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
29
2005
On the multi-grid method applied to difference equations. Zbl 0391.65045
Hackbusch, W.
28
1978
Convergence of multi-grid iterations applied to difference equations. Zbl 0422.65020
Hackbusch, Wolfgang
28
1980
\(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
27
2002
Composite finite elements for problems containing small geometric details. II: Implementation and numerical results. Zbl 1001.65127
Hackbusch, W.; Sauter, S. A.
27
1997
Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
27
2004
On the nonlinear domain decomposition method. Zbl 0891.65126
Dryja, M.; Hackbusch, W.
26
1997
Sparse convolution quadrature for time domain boundary integral formulations of the wave equation. Zbl 1178.65121
Hackbusch, W.; Kress, W.; Sauter, S. A.
26
2009
Tensor-product approximation to operators and functions in high dimensions. Zbl 1141.65032
Hackbusch, Wolfgang; Khoromskij, Boris N.
24
2007
On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method. Zbl 0403.65043
Hackbusch, W.
23
1979
On multi-grid methods for variational inequalities. Zbl 0497.65042
Hackbusch, W.; Mittelmann, H. D.
23
1983
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats. Zbl 1350.65005
Espig, Mike; Hackbusch, Wolfgang; Litvinenko, Alexander; Matthies, Hermann G.; Wähnert, Philipp
23
2014
Analysis of a damped nonlinear multilevel method. Zbl 0673.65031
Hackbusch, Wolfgang; Reusken, Arnold
22
1989
On the efficient use of the Galerkin-method to solve Fredholm integral equations. Zbl 0791.65101
Hackbusch, Wolfgang; Sauter, Stefan A.
21
1993
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems. Zbl 1149.78009
Banjai, Lehel; Hackbusch, Wolfgang
21
2008
On minimal subspaces in tensor representations. Zbl 1260.15040
Falcó, Antonio; Hackbusch, Wolfgang
21
2012
Elliptic differential equations. Theory and numerical treatment. 2nd edition. Zbl 1379.35001
Hackbusch, Wolfgang
21
2017
On numerical cubatures of nearly singular surface integrals arising in BEM collocation. Zbl 0799.65028
Hackbusch, Wolfgang; Sauter, Stefan A.
20
1994
Integralgleichungen. Theorie und Numerik. (Integral equations. Theory and numerics). Zbl 0681.65099
Hackbusch, Wolfgang
19
1989
Numerical tensor calculus. Zbl 1396.65091
Hackbusch, Wolfgang
19
2014
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators. Zbl 1087.65050
Hackbusch, W.; Khoromskij, B. N.
19
2006
Local defect correction method and domain decomposition techniques. Zbl 0552.65070
Hackbusch, W.
18
1984
The frequency decomposition multi-grid method. I: Application to anisotropic equations. Zbl 0673.65062
Hackbusch, Wolfgang
18
1989
An introduction to hierarchical matrices. Zbl 1007.65032
Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen
18
2002
On the convergence of multi-grid iterations. Zbl 0465.65054
Hackbusch, Wolfgang
18
1981
Iterative solution of large sparse systems of equations. 2nd edition. Zbl 1347.65063
Hackbusch, Wolfgang
18
2016
Multigrid methods. Proceedings of the Conference Held at Köln-Porz, November 23-27, 1981. Zbl 0497.00015
17
1982
Use of tensor formats in elliptic eigenvalue problems. Zbl 1274.35252
Hackbusch, Wolfgang; Khoromskij, Boris N.; Sauter, Stefan; Tyrtyshnikov, Eugene E.
17
2012
An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples. Zbl 1283.15075
Grasedyck, Lars; Hackbusch, Wolfgang
16
2011
A multigrid method to solve large scale Sylvester equations. Zbl 1154.65024
Grasedyck, Lars; Hackbusch, Wolfgang
16
2007
Black box low tensor-rank approximation using fiber-crosses. Zbl 1181.65064
Espig, Mike; Grasedyck, Lars; Hackbusch, Wolfgang
16
2009
Sparse convolution quadrature for time domain boundary integral formulations of the wave equation by cutoff and panel-clustering. Zbl 1298.65185
Hackbusch, Wolfgang; Kress, Wendy; Sauter, Stefan A.
15
2007
On the fast solving of parabolic boundary control problems. Zbl 0402.49025
Hackbusch, Wolfgang
15
1979
Fast solution of elliptic control problems. Zbl 0417.49041
Hackbusch, W.
14
1980
Variational calculus with sums of elementary tensors of fixed rank. Zbl 1259.65090
Espig, Mike; Hackbusch, Wolfgang; Rohwedder, Thorsten; Schneider, Reinhold
14
2012
A multigrid method for nonconforming FE-discretisations with application to non-matching grids. Zbl 0931.65120
Braess, Dietrich; Dryja, M.; Hackbusch, W.
13
1999
Parabolic multi-grid methods. Zbl 0565.65062
Hackbusch, Wolfgang
13
1984
A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format. Zbl 1264.65087
Espig, Mike; Hackbusch, Wolfgang
12
2012
Additive and multiplicative multi-grid – a comparison. Zbl 0908.65107
Bastian, P.; Hackbusch, W.; Wittum, G.
11
1998
On the regularity of difference schemes. Zbl 0462.65058
Hackbusch, Wolfgang
11
1981
Performance of H-LU preconditioning for sparse matrices. Zbl 1156.65042
Grasedyck, L.; Hackbusch, W.; Kriemann, R.
11
2008
Tensorisation of vectors and their efficient convolution. Zbl 1236.15054
Hackbusch, Wolfgang
10
2011
Iterative solution of large sparse systems of equations. 2., überarb. u. erw. Aufl. (Iterative Lösung großer schwachbesetzter Gleichungssysteme.) Zbl 0861.65022
Hackbusch, Wolfgang
10
1993
Downwind Gauss-Seidel smoothing for convection dominated problems. Zbl 0889.65026
Hackbusch, W.; Probst, T.
10
1997
Optimization problems in contracted tensor networks. Zbl 1380.49059
Espig, Mike; Hackbusch, Wolfgang; Handschuh, Stefan; Schneider, Reinhold
10
2011
Best \(N\)-term approximation in electronic structure calculations. I: One-electron reduced density matrix. Zbl 1100.81050
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold
10
2006
Iterative Lösung großer schwachbesetzter Gleichungssysteme. (Iterative solution of large sparse systems of equations). Zbl 0729.65018
Hackbusch, Wolfgang
9
1991
On the efficient evaluation of coalescence integrals in population balance models. Zbl 1104.65023
Hackbusch, W.
9
2006
Towards \(\mathcal H\)-matrix approximation of linear complexity. Zbl 1004.65125
Hackbusch, Wolfgang; Khoromskij, Boris N.
9
2001
Fast numerical solution of time-periodic parabolic problems by a multigrid method. Zbl 0483.65062
Hackbusch, Wolfgang
9
1981
Optimal H(p’,p/2) error estimates for a parabolic Galerkin method. Zbl 0483.65063
Hackbusch, W.
9
1981
Dis schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art. Zbl 0458.65108
Hackbusch, Wolfgang
9
1981
Efficient convolution with the Newton potential in \(d\) dimensions. Zbl 1161.65018
Hackbusch, W.
9
2008
Multigrid methods II. Proceedings of the 2nd European Conference on Multigrid Methods held at Cologne (Federal Republic of Germany), October 1-4, 1985. Zbl 0596.00016
8
1986
Comparison of different multi-grid variants for nonlinear equations. Zbl 0766.65044
Hackbusch, Wolfgang
8
1992
Multi-grid convergence theory. Zbl 0505.65036
Hackbusch, W.
8
1982
Numerical mathematics of the subtraction method for the modeling of a current dipole in EEG source reconstruction using finite element head models. Zbl 1159.92029
Wolters, C. H.; Köstler, H.; Möller, C.; Härdtlein, J.; Grasedyck, L.; Hackbusch, W.
8
2007
On the regularity of difference schemes. II: Regularity estimates for linear and nonlinear problems. Zbl 0535.65071
Hackbusch, Wolfgang
7
1983
Construction and complexity of hierarchical matrices. Zbl 1201.65043
Grasedyck, Lars; Hackbusch, Wolfgang
7
2003
The efficient computation of certain determinants arising in the treatment of Schrödinger’s equations. Zbl 0997.65075
Hackbusch, W.
7
2001
Direct integration of the Newton potential over cubes. Zbl 1009.65070
Hackbusch, Wolfgang
7
2002
Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
7
2000
Stabilized rounded addition of hierarchical matrices. Zbl 1199.65135
Bebendorf, M.; Hackbusch, W.
7
2007
Fast and exact projected convolution for non-equidistant grids. Zbl 1124.65119
Hackbusch, W.
7
2007
Truncation of tensors in the hierarchical format. Zbl 1479.15027
Hackbusch, Wolfgang
1
2021
Iterative algorithms for the post-processing of high-dimensional data. Zbl 1436.65054
Espig, Mike; Hackbusch, Wolfgang; Litvinenko, Alexander; Matthies, Hermann G.; Zander, Elmar
1
2020
Tensor spaces and numerical tensor calculus. 2nd revised edition. Zbl 07150978
Hackbusch, Wolfgang
6
2019
On the Dirac-Frenkel variational principle on tensor Banach spaces. Zbl 1427.46013
Falcó, Antonio; Hackbusch, Wolfgang; Nouy, Anthony
6
2019
On the representation of symmetric and antisymmetric tensors. Zbl 1405.15034
Hackbusch, Wolfgang
1
2018
Elliptic differential equations. Theory and numerical treatment. 2nd edition. Zbl 1379.35001
Hackbusch, Wolfgang
21
2017
On the interconnection between the higher-order singular values of real tensors. Zbl 1364.15018
Hackbusch, Wolfgang; Uschmajew, André
6
2017
Perturbation of higher-order singular values. Zbl 1371.15011
Hackbusch, Wolfgang; Kressner, Daniel; Uschmajew, André
3
2017
Iterative solution of large sparse systems of equations. 2nd edition. Zbl 1347.65063
Hackbusch, Wolfgang
18
2016
New estimates for the recursive low-rank truncation of block-structured matrices. Zbl 1333.65046
Hackbusch, Wolfgang
5
2016
Survey on the technique of hierarchical matrices. Zbl 1336.65028
Hackbusch, Wolfgang
3
2016
Preface: Special issue dedicated to Eberhard Zeidler’s 75th birthday. Zbl 1334.00106
1
2016
Hierarchical matrices: algorithms and analysis. Zbl 1336.65041
Hackbusch, Wolfgang
97
2015
Solution of linear systems in high spatial dimensions. Zbl 1388.65032
Hackbusch, Wolfgang
7
2015
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats. Zbl 1350.65005
Espig, Mike; Hackbusch, Wolfgang; Litvinenko, Alexander; Matthies, Hermann G.; Wähnert, Philipp
23
2014
Numerical tensor calculus. Zbl 1396.65091
Hackbusch, Wolfgang
19
2014
Tensor spaces and hierarchical tensor representations. Zbl 1317.65102
Hackbusch, Wolfgang; Schneider, Reinhold
6
2014
The concept of stability in numerical mathematics. Zbl 1321.65139
Hackbusch, Wolfgang
2
2014
\(L^{\infty}\) estimation of tensor truncations. Zbl 1282.65046
Hackbusch, Wolfgang
6
2013
Tensor spaces and numerical tensor calculus. Zbl 1244.65061
Hackbusch, Wolfgang
218
2012
On minimal subspaces in tensor representations. Zbl 1260.15040
Falcó, Antonio; Hackbusch, Wolfgang
21
2012
Use of tensor formats in elliptic eigenvalue problems. Zbl 1274.35252
Hackbusch, Wolfgang; Khoromskij, Boris N.; Sauter, Stefan; Tyrtyshnikov, Eugene E.
17
2012
Variational calculus with sums of elementary tensors of fixed rank. Zbl 1259.65090
Espig, Mike; Hackbusch, Wolfgang; Rohwedder, Thorsten; Schneider, Reinhold
14
2012
A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format. Zbl 1264.65087
Espig, Mike; Hackbusch, Wolfgang
12
2012
A numerical method for the simulation of an aggregation-driven population balance system. Zbl 1253.76024
Hackbusch, Wolfgang; John, Volker; Khachatryan, Aram; Suciu, Carina
1
2012
An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples. Zbl 1283.15075
Grasedyck, Lars; Hackbusch, Wolfgang
16
2011
Tensorisation of vectors and their efficient convolution. Zbl 1236.15054
Hackbusch, Wolfgang
10
2011
Optimization problems in contracted tensor networks. Zbl 1380.49059
Espig, Mike; Hackbusch, Wolfgang; Handschuh, Stefan; Schneider, Reinhold
10
2011
Elliptic differential equations: theory and numerical treatment. Transl. from the German by Regine Fadiman and Patrick D. F. Ion. Paperback reprint of 1992 hardback edition. Zbl 1205.35060
Hackbusch, Wolfgang
30
2010
Concepts of data-sparse tensor-product approximation in many-particle modelling. Zbl 1214.81077
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Khoromskij, Boris N.; Schneider, Reinhold
4
2010
Efficient multi-scale computation of products of orbitals in electronic structure calculations. Zbl 1237.65016
Chinnamsetty, Sambasiva Rao; Hackbusch, Wolfgang; Flad, Heinz-Jürgen
2
2010
A new scheme for the tensor representation. Zbl 1188.15022
Hackbusch, W.; Kühn, S.
118
2009
Hierarchical matrices. Algorithms and analysis. (Hierarchische Matrizen. Algorithmen und Analysis.) Zbl 1180.65004
Hackbusch, Wolfgang
40
2009
On the efficient computation of high-dimensional integrals and the approximation by exponential sums. Zbl 1190.65036
Braess, Dietrich; Hackbusch, Wolfgang
31
2009
Sparse convolution quadrature for time domain boundary integral formulations of the wave equation. Zbl 1178.65121
Hackbusch, W.; Kress, W.; Sauter, S. A.
26
2009
Black box low tensor-rank approximation using fiber-crosses. Zbl 1181.65064
Espig, Mike; Grasedyck, Lars; Hackbusch, Wolfgang
16
2009
Convolution of \(hp\)-functions on locally refined grids. Zbl 1181.65041
Hackbusch, W.
6
2009
Preconditioning by inverting the Laplacian: An analysis of the eigenvalues. Zbl 1167.65066
Nielsen, Bjørn Fredrik; Tveito, Aslak; Hackbusch, Wolfgang
4
2009
Approximate iterations for structured matrices. Zbl 1144.65029
Hackbusch, Wolfgang; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E.
40
2008
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems. Zbl 1149.78009
Banjai, Lehel; Hackbusch, Wolfgang
21
2008
Performance of H-LU preconditioning for sparse matrices. Zbl 1156.65042
Grasedyck, L.; Hackbusch, W.; Kriemann, R.
11
2008
Efficient convolution with the Newton potential in \(d\) dimensions. Zbl 1161.65018
Hackbusch, W.
9
2008
Tensor-product approximation to multidimensional integral operators and Green’s functions. Zbl 1171.65099
Hackbusch, Wolfgang; Khoromskij, Boris N.
6
2008
Numerical method for elliptic multiscale problems. Zbl 1151.65095
Greff, I.; Hackbusch, W.
1
2008
Optimal panel-clustering in the presence of anisotropic mesh refinement. Zbl 1160.65062
Graham, I. G.; Grasedyck, L.; Hackbusch, W.; Sauter, S. A.
1
2008
Tensor-product approximation to operators and functions in high dimensions. Zbl 1141.65032
Hackbusch, Wolfgang; Khoromskij, Boris N.
24
2007
A multigrid method to solve large scale Sylvester equations. Zbl 1154.65024
Grasedyck, Lars; Hackbusch, Wolfgang
16
2007
Sparse convolution quadrature for time domain boundary integral formulations of the wave equation by cutoff and panel-clustering. Zbl 1298.65185
Hackbusch, Wolfgang; Kress, Wendy; Sauter, Stefan A.
15
2007
Numerical mathematics of the subtraction method for the modeling of a current dipole in EEG source reconstruction using finite element head models. Zbl 1159.92029
Wolters, C. H.; Köstler, H.; Möller, C.; Härdtlein, J.; Grasedyck, L.; Hackbusch, W.
8
2007
Stabilized rounded addition of hierarchical matrices. Zbl 1199.65135
Bebendorf, M.; Hackbusch, W.
7
2007
Fast and exact projected convolution for non-equidistant grids. Zbl 1124.65119
Hackbusch, W.
7
2007
Best \(N\)-term approximation in electronic structure calculations. II: Jastrow factors. Zbl 1135.81029
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold
7
2007
Approximation of coalescence integrals in population balance models with local mass conservation. Zbl 1116.65130
Hackbusch, Wolfgang
5
2007
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions. Zbl 1087.65049
Hackbusch, W.; Khoromskij, B. N.
51
2006
Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators. Zbl 1087.65050
Hackbusch, W.; Khoromskij, B. N.
19
2006
Best \(N\)-term approximation in electronic structure calculations. I: One-electron reduced density matrix. Zbl 1100.81050
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold
10
2006
On the efficient evaluation of coalescence integrals in population balance models. Zbl 1104.65023
Hackbusch, W.
9
2006
Approximation of \(1/\| x-y \|\) by exponentials for wavelet applications. Zbl 1095.65107
Hackbusch, W.
2
2006
Coarsening of boundary-element spaces. Zbl 1092.65108
Hackbusch, W.; Löhndorf, M.; Sauter, S. A.
2
2006
Approximation of \(1/x\) by exponential sums in \([1, \infty]\). Zbl 1082.65025
Braess, Dietrich; Hackbusch, Wolfgang
42
2005
Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
41
2005
Hierarchical Kronecker tensor-product approximations. Zbl 1081.65035
Hackbusch, W.; Khoromskij, B. N.; Tyrtyshnikov, E. E.
39
2005
Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
36
2005
Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
29
2005
Hierarchical quadrature for singular integrals. Zbl 1068.65038
Börm, S.; Hackbusch, W.
5
2005
Direct Schur complement method by hierarchical matrix techniques. Zbl 1066.65143
Hackbusch, Wolfgang; Khoromskij, Boris N.; Kriemann, Ronald
3
2005
Wavelet approach to quasi two-dimensional extended many-particle systems. I: Supercell Hartree-Fock method. Zbl 1088.82029
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Luo, Hongjun; Kolb, Dietmar
1
2005
Hierarchical matrices based on a weak admissibility criterion. Zbl 1063.65035
Hackbusch, W.; Khoromskij, B. N.; Kriemann, R.
36
2004
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110
Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A.
34
2004
Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
27
2004
Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem. Zbl 1075.92039
Wolters, C. H.; Grasedyck, L.; Hackbusch, W.
6
2004
Adaptive geometrically balanced clustering of \({\mathcal H}\)-matrices. Zbl 1063.65031
Grasedyck, L.; Hackbusch, W.; Le Borne, S.
6
2004
Approximation of boundary element operators by adaptive \({\mathcal H}^2\)-matrices. Zbl 1097.65119
Börm, Steffen; Hackbusch, Wolfgang
3
2004
Construction and arithmetics of \(\mathcal H\)-matrices. Zbl 1030.65033
Grasedyck, Lars; Hackbusch, Wolfgang
126
2003
Introduction to hierarchical matrices with applications. Zbl 1035.65042
Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang
98
2003
Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients. Zbl 1033.65100
Bebendorf, Mario; Hackbusch, Wolfgang
75
2003
Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Zbl 1239.65026
Grasedyck, Lars; Hackbusch, Wolfgang; Khoromskij, B. N.
43
2003
Construction and complexity of hierarchical matrices. Zbl 1201.65043
Grasedyck, Lars; Hackbusch, Wolfgang
7
2003
Computational electromagnetics. Proceedings of the GAMM workshop on computational electromagnetics, Kiel, Germany, January 26–28, 2001. Zbl 1007.78001
5
2003
Low-rank approximation of FE matrix inverses for operators with jumping coefficients. Zbl 1201.65041
Bebendorf, M.; Hackbusch, W.
1
2003
Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices. Zbl 1012.65023
Hackbusch, W.; Börm, S.
60
2002
\(\mathcal H^2\)-matrix approximation of integral operators by interpolation. Zbl 1019.65103
Hackbusch, Wolfgang; Börm, Steffen
39
2002
\(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N.
27
2002
An introduction to hierarchical matrices. Zbl 1007.65032
Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen
18
2002
Direct integration of the Newton potential over cubes. Zbl 1009.65070
Hackbusch, Wolfgang
7
2002
Blended kernel approximation in the \({\mathcal {H}}\)-matrix techniques. Zbl 1071.65553
Hackbusch, W.; Khoromskij, B. N.
1
2002
Towards \(\mathcal H\)-matrix approximation of linear complexity. Zbl 1004.65125
Hackbusch, Wolfgang; Khoromskij, Boris N.
9
2001
The efficient computation of certain determinants arising in the treatment of Schrödinger’s equations. Zbl 0997.65075
Hackbusch, W.
7
2001
\(\mathcal H\)-matrix approximation for elliptic solution operators in cylinder domains. Zbl 1012.65134
Gavrilyuk, I. P.; Hackbusch, W.; Khoromskij, B. N.
6
2001
A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems. Zbl 0962.65029
Hackbusch, W.; Khoromskij, B. N.
121
2000
On \({\mathcal H}^2\)-matrices. Zbl 0963.65043
Hackbusch, W.; Khoromskij, B.; Sauter, S. A.
53
2000
A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates. Zbl 0977.65036
Hackbusch, W.; Khoromskij, B. N.
29
2000
Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
7
2000
Discrete boundary element methods on general meshes in 3D. Zbl 0966.65090
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
5
2000
Hybrid Galerkin boundary elements on degenerate meshes. Zbl 0937.65127
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2
2000
\(\mathcal H\)-matrix approximation on graded meshes. Zbl 0960.65047
Hackbusch, Wolfgang; Khoronskij, Boris N.
1
2000
A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices. Zbl 0927.65063
Hackbusch, W.
293
1999
A multigrid method for nonconforming FE-discretisations with application to non-matching grids. Zbl 0931.65120
Braess, Dietrich; Dryja, M.; Hackbusch, W.
13
1999
Additive and multiplicative multi-grid – a comparison. Zbl 0908.65107
Bastian, P.; Hackbusch, W.; Wittum, G.
11
1998
A new finite element approach for problems containing small geometric details. Zbl 0912.65088
Hackbusch, W.; Sauter, S. A.
4
1998
...and 82 more Documents
all top 5

Cited by 3,232 Authors

79 Hackbusch, Wolfgang
44 Khoromskiĭ, Boris Nikolaevich
35 Harbrecht, Helmut
34 Praetorius, Dirk
30 Sauter, Stefan A.
30 Schneider, Reinhold
26 Kressner, Daniel
24 Börm, Steffen
24 Wittum, Gabriel
23 Oseledets, Ivan V.
20 Benner, Peter
20 Grasedyck, Lars
20 Tyrtyshnikov, Evgeniĭ Evgen’evich
20 Xu, Jinchao
18 Ying, Lexing
17 Bebendorf, Mario
17 Brenner, Susanne Cecelia
17 Keyes, David Elliot
17 Melenk, Jens Markus
16 Griebel, Michael
16 Le Borne, Sabine
16 Yserentant, Harry
15 Darve, Eric
15 Dolgov, Sergey V.
15 Nouy, Anthony
15 Schwab, Christoph
15 Stevenson, Rob P.
15 Xia, Jianlin
14 Borzì, Alfio
13 Dölz, Jürgen
13 Gaspar, Francisco José
13 Matthies, Hermann Georg
13 Vassilevski, Panayot Spirov
12 Axelsson, Axel Owe Holger
12 Martinsson, Per-Gunnar
12 Oosterlee, Cornelis Willebrordus
12 Uschmajew, André
11 Bachmayr, Markus
11 Chen, Chuanjun
11 Dahmen, Wolfgang A.
11 Feischl, Michael
11 Führer, Thomas
11 Gillman, Adrianna
11 Karkulik, Michael
11 Khoromskaia, Venera
11 Lubich, Christian
11 Mandel, Jan
11 Pasciak, Joseph E.
11 Rodrigo, Carmen
11 Turkiyyah, George M.
11 Zou, Qingsong
10 Gavrilyuk, Ivan P.
10 Greengard, Leslie F.
10 Lenhart, Suzanne M.
10 Xie, Hehu
9 Antonietti, Paola Francesca
9 Bank, Randolph E.
9 Chaillat, Stéphanie
9 Chen, Ke
9 Giani, Stefano
9 Hoppe, Ronald H. W.
9 Houston, Paul
9 Li, Jichun
9 Massei, Stefano
9 Notay, Yvan
9 Ravnik, Jure
9 Simoncini, Valeria
9 Stoll, Martin
9 Vandewalle, Stefan G.
8 Aimi, Alessandra
8 Ballani, Jonas
8 Banjai, Lehel
8 Braess, Dietrich
8 Eigel, Martin
8 Espig, Mike
8 Gander, Martin Jakob
8 Ho, Kenneth L.
8 Karátson, János
8 Kraus, Johannes K.
8 Li, Xiaoye Sherry
8 Of, Günther
8 Rüde, Ulrich
8 Saad, Yousef
8 Tausch, Johannes
8 Wang, Hong
8 Wohlmuth, Barbara I.
8 Xiao, Jinyou
8 Zikatanov, Ludmil T.
8 Zulehner, Walter
7 Aurada, Markus
7 Bramble, James H.
7 Diligenti, Mauro
7 Elman, Howard C.
7 Falcó, Antonio
7 Falletta, Silvia
7 Ferraz-Leite, Samuel
7 Genton, Marc G.
7 Huang, Qiumei
7 Litvinenko, Alexander
7 Lu, Jianfeng
...and 3,132 more Authors
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Cited in 283 Serials

182 Journal of Computational Physics
170 Numerische Mathematik
144 SIAM Journal on Scientific Computing
141 Journal of Computational and Applied Mathematics
109 Computer Methods in Applied Mechanics and Engineering
95 Applied Numerical Mathematics
86 Mathematics of Computation
86 Computing
84 Applied Mathematics and Computation
71 Computers & Mathematics with Applications
71 Numerical Linear Algebra with Applications
66 Engineering Analysis with Boundary Elements
56 Journal of Scientific Computing
54 SIAM Journal on Matrix Analysis and Applications
47 International Journal for Numerical Methods in Engineering
45 Computing and Visualization in Science
41 BIT
41 Linear Algebra and its Applications
38 Numerical Algorithms
37 Advances in Computational Mathematics
32 SIAM Journal on Numerical Analysis
27 International Journal for Numerical Methods in Fluids
27 Numerical Methods for Partial Differential Equations
25 Numerical Functional Analysis and Optimization
24 Computational Mechanics
24 Computational Methods in Applied Mathematics
19 Journal of Integral Equations and Applications
19 Multiscale Modeling & Simulation
18 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
17 International Journal of Computer Mathematics
16 SIAM/ASA Journal on Uncertainty Quantification
15 Journal of Numerical Mathematics
14 RAIRO. Modélisation Mathématique et Analyse Numérique
13 Calcolo
13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
12 Computational Optimization and Applications
10 Computers and Fluids
10 Inverse Problems
10 Mathematics and Computers in Simulation
10 Journal of Complexity
10 Applications of Mathematics
10 Mathematical Problems in Engineering
10 Foundations of Computational Mathematics
9 Computer Physics Communications
9 Applied Mathematics Letters
9 SIAM Review
9 Applied and Computational Harmonic Analysis
9 Computational Geosciences
9 Archives of Computational Methods in Engineering
8 Constructive Approximation
7 Mathematical Methods in the Applied Sciences
7 Computational Mathematics and Mathematical Physics
7 Applied Mathematical Modelling
7 Advances in Applied Mathematics and Mechanics
6 Journal of Engineering Mathematics
6 Mathematical Biosciences
6 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
6 Journal of Optimization Theory and Applications
6 Mathematical Programming. Series A. Series B
6 Vietnam Journal of Mathematics
6 Optimization Methods & Software
6 Acta Numerica
6 Science China. Mathematics
6 Statistics and Computing
5 Journal of Mathematical Analysis and Applications
5 Zeitschrift für Analysis und ihre Anwendungen
5 COMPEL
5 Computational and Applied Mathematics
5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
5 Discrete and Continuous Dynamical Systems. Series B
5 Communications in Computational Physics
5 SIAM Journal on Imaging Sciences
5 S\(\vec{\text{e}}\)MA Journal
4 Archive for Rational Mechanics and Analysis
4 Journal of Mathematical Biology
4 Wave Motion
4 Bulletin of Mathematical Biology
4 Computational Statistics and Data Analysis
4 SIAM Journal on Optimization
4 Communications in Numerical Methods in Engineering
4 Journal of Applied Mathematics and Computing
4 PAMM. Proceedings in Applied Mathematics and Mechanics
4 Journal of Computational and Graphical Statistics
4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Applicable Analysis
3 Communications on Pure and Applied Mathematics
3 Journal of Statistical Physics
3 Linear and Multilinear Algebra
3 Applied Mathematics and Optimization
3 SIAM Journal on Control and Optimization
3 Physica D
3 Science in China. Series A
3 SIAM Journal on Mathematical Analysis
3 Journal of Mathematical Imaging and Vision
3 Journal of Inverse and Ill-Posed Problems
3 Journal of Mathematical Chemistry
3 Doklady Mathematics
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Mediterranean Journal of Mathematics
...and 183 more Serials
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Cited in 51 Fields

2,230 Numerical analysis (65-XX)
983 Partial differential equations (35-XX)
313 Fluid mechanics (76-XX)
279 Linear and multilinear algebra; matrix theory (15-XX)
212 Mechanics of deformable solids (74-XX)
164 Calculus of variations and optimal control; optimization (49-XX)
143 Integral equations (45-XX)
120 Optics, electromagnetic theory (78-XX)
84 Computer science (68-XX)
84 Biology and other natural sciences (92-XX)
80 Approximations and expansions (41-XX)
75 Probability theory and stochastic processes (60-XX)
64 Operator theory (47-XX)
62 Operations research, mathematical programming (90-XX)
55 Statistics (62-XX)
50 Statistical mechanics, structure of matter (82-XX)
49 Systems theory; control (93-XX)
41 Quantum theory (81-XX)
38 Ordinary differential equations (34-XX)
34 Functional analysis (46-XX)
31 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
29 Information and communication theory, circuits (94-XX)
25 Harmonic analysis on Euclidean spaces (42-XX)
24 Potential theory (31-XX)
24 Geophysics (86-XX)
23 Real functions (26-XX)
23 Classical thermodynamics, heat transfer (80-XX)
19 Integral transforms, operational calculus (44-XX)
14 Dynamical systems and ergodic theory (37-XX)
12 Algebraic geometry (14-XX)
11 Combinatorics (05-XX)
10 Global analysis, analysis on manifolds (58-XX)
9 Mechanics of particles and systems (70-XX)
8 General and overarching topics; collections (00-XX)
8 Special functions (33-XX)
8 Difference and functional equations (39-XX)
8 Differential geometry (53-XX)
6 Astronomy and astrophysics (85-XX)
4 Functions of a complex variable (30-XX)
3 Measure and integration (28-XX)
2 History and biography (01-XX)
2 Mathematical logic and foundations (03-XX)
2 Commutative algebra (13-XX)
2 Convex and discrete geometry (52-XX)
1 Number theory (11-XX)
1 Field theory and polynomials (12-XX)
1 Associative rings and algebras (16-XX)
1 Sequences, series, summability (40-XX)
1 General topology (54-XX)
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1 Mathematics education (97-XX)

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