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ORCIDWolfgang Hackbusch
Person information
- affiliation: Max-Planck-Institut Mathematik in den Naturwissenschaften, Leipzig, Germany
- award (1994): Gottfried Wilhelm Leibniz Prize
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2020 – today
- 2020
[j75]Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko
, Hermann G. Matthies, Elmar Zander:
Iterative algorithms for the post-processing of high-dimensional data. J. Comput. Phys. 410: 109396 (2020)- [i2]Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy:
Geometry of tree-based tensor formats in tensor Banach spaces. CoRR abs/2011.08466 (2020)
2010 – 2019
- 2019
- [j74]Wolfgang Hackbusch:
Computation of best L∞ exponential sums for 1 / x by Remez' algorithm. Comput. Vis. Sci. 20(1-2): 1-11 (2019) - [j73]Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy:
On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces. Found. Comput. Math. 19(1): 159-204 (2019) - [i1]Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann G. Matthies, Elmar Zander:
Post-Processing of High-Dimensional Data. CoRR abs/1906.05669 (2019) - 2017
- [j72]Wolfgang Hackbusch, André Uschmajew:
On the interconnection between the higher-order singular values of real tensors. Numerische Mathematik 135(3): 875-894 (2017) - [j71]Wolfgang Hackbusch, Daniel Kressner, André Uschmajew:
Perturbation of Higher-Order Singular Values. SIAM J. Appl. Algebra Geom. 1(1): 374-387 (2017) - 2016
- [j70]Wolfgang Hackbusch:
New estimates for the recursive low-rank truncation of block-structured matrices. Numerische Mathematik 132(2): 303-328 (2016) - 2015
- [j69]Wolfgang Hackbusch:
Solution of linear systems in high spatial dimensions. Comput. Vis. Sci. 17(3): 111-118 (2015) - [j68]Sambasiva Rao Chinnamsetty, Mike Espig, Wolfgang Hackbusch:
Mesh-free canonical tensor products for six-dimensional density matrix: computation of kinetic energy. Comput. Vis. Sci. 17(6): 267-275 (2015) - 2014
- [j67]Wolfgang Hackbusch:
Numerical tensor calculus. Acta Numer. 23: 651-742 (2014) - [j66]Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann G. Matthies, Philipp Wähnert:
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats. Comput. Math. Appl. 67(4): 818-829 (2014) - 2013
- [j65]Wolfgang Hackbusch:
L∞ estimation of tensor truncations. Numerische Mathematik 125(3): 419-440 (2013) - 2012
- [j64]Wolfgang Hackbusch, Florian Drechsler:
Partial evaluation of the discrete solution of elliptic boundary value problems. Comput. Vis. Sci. 15(5): 227-245 (2012) - [j63]Antonio Falcó, Wolfgang Hackbusch:
On Minimal Subspaces in Tensor Representations. Found. Comput. Math. 12(6): 765-803 (2012) - [j62]Matthias Borchardt, Ralf Kleiber, Wolfgang Hackbusch:
A fast solver for the gyrokinetic field equation with adiabatic electrons. J. Comput. Phys. 231(18): 6207-6212 (2012) - [j61]Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter, Eugene E. Tyrtyshnikov:
Use of tensor formats in elliptic eigenvalue problems. Numer. Linear Algebra Appl. 19(1): 133-151 (2012) - [j60]Mike Espig, Wolfgang Hackbusch, Thorsten Rohwedder, Reinhold Schneider:
Variational calculus with sums of elementary tensors of fixed rank. Numerische Mathematik 122(3): 469-488 (2012) - [j59]Mike Espig, Wolfgang Hackbusch:
A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format. Numerische Mathematik 122(3): 489-525 (2012) - 2011
- [j58]Lars Grasedyck, Wolfgang Hackbusch:
An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples. Comput. Methods Appl. Math. 11(3): 291-304 (2011) - [j57]Mike Espig, Wolfgang Hackbusch, Stefan Handschuh, Reinhold Schneider:
Optimization problems in contracted tensor networks. Comput. Vis. Sci. 14(6): 271-285 (2011) - [j56]Volodymyr P. Sergiievskyi, Wolfgang Hackbusch, Maxim V. Fedorov:
Multigrid solver for the reference interaction site model of molecular liquids theory. J. Comput. Chem. 32(9): 1982-1992 (2011) - [j55]Wolfgang Hackbusch:
Tensorisation of vectors and their efficient convolution. Numerische Mathematik 119(3): 465 (2011) - 2010
- [j54]Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch, Heinz-Jürgen Flad:
Efficient multi-scale computation of products of orbitals in electronic structure calculations. Comput. Vis. Sci. 13(8): 397-408 (2010) - [j53]Wolfgang Hackbusch, Kishore Kumar Naraparaju, Jan Schneider:
On the efficient convolution with the Newton potential. J. Num. Math. 18(4): 257-280 (2010)
2000 – 2009
- 2008
- [j52]Jürgen Koch, Wolfgang Hackbusch, Kai Sundmacher:
H-matrix methods for quadratic integral operators appearing in population balances. Comput. Chem. Eng. 32(8): 1789-1809 (2008) - [j51]Isabelle Greff, Wolfgang Hackbusch:
Numerical method for elliptic multiscale problems. J. Num. Math. 16(2): 119-138 (2008) - [j50]Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov:
Approximate iterations for structured matrices. Numerische Mathematik 109(3): 365-383 (2008) - [j49]Wolfgang Hackbusch:
Efficient convolution with the Newton potential in d dimensions. Numerische Mathematik 110(4): 449-489 (2008) - [j48]Wolfgang Hackbusch, Boris N. Khoromskij:
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions. SIAM J. Matrix Anal. Appl. 30(3): 1233-1253 (2008) - 2007
- [j47]Jürgen Koch, Wolfgang Hackbusch, Kai Sundmacher:
H-matrix methods for linear and quasi-linear integral operators appearing in population balances. Comput. Chem. Eng. 31(7): 745-759 (2007) - [j46]Wolfgang Hackbusch:
Fast and exact projected convolution for non-equidistant grids. Computing 80(2): 137-168 (2007) - [j45]Wolfgang Hackbusch, W. Kress:
A projection method for the computation of inner eigenvalues using high degree rational operators. Computing 81(4): 259-268 (2007) - [j44]Wolfgang Hackbusch, Boris N. Khoromskij:
Tensor-product approximation to operators and functions in high dimensions. J. Complex. 23(4-6): 697-714 (2007) - [j43]Mario Bebendorf, Wolfgang Hackbusch:
Stabilized rounded addition of hierarchical matrices. Numer. Linear Algebra Appl. 14(5): 407-423 (2007) - [j42]Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter:
Adaptive Galerkin boundary element methods with panel clustering. Numerische Mathematik 105(4): 603-631 (2007) - [j41]Wolfgang Hackbusch:
Approximation of coalescence integrals in population balance models with local mass conservation. Numerische Mathematik 106(4): 627-657 (2007) - [j40]Lars Grasedyck, Wolfgang Hackbusch:
A Multigrid Method to Solve Large Scale Sylvester Equations. SIAM J. Matrix Anal. Appl. 29(3): 870-894 (2007) - [j39]Ivan G. Graham, Lars Grasedyck, Wolfgang Hackbusch, Stefan A. Sauter:
Optimal Panel-Clustering in the Presence of Anisotropic Mesh Refinement. SIAM J. Numer. Anal. 46(1): 517-543 (2007) - [j38]Carsten H. Wolters, Harald Köstler, Christian Möller, Jochen Härdtlein, Lars Grasedyck, Wolfgang Hackbusch:
Numerical Mathematics of the Subtraction Method for the Modeling of a Current Dipole in EEG Source Reconstruction Using Finite Element Head Models. SIAM J. Sci. Comput. 30(1): 24-45 (2007) - 2006
- [j37]Wolfgang Hackbusch, Boris N. Khoromskij:
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions. Computing 76(3-4): 177-202 (2006) - [j36]Wolfgang Hackbusch, Boris N. Khoromskij:
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators. Computing 76(3-4): 203-225 (2006) - [j35]Wolfgang Hackbusch:
Approximation of 1/||x-y|| by Exponentials for Wavelet Applications (Short Communication). Computing 76(3-4): 359-366 (2006) - [j34]Wolfgang Hackbusch, M. Löhndorf, Stefan A. Sauter:
Coarsening of Boundary-element Spaces. Computing 77(3): 253-273 (2006) - [j33]Wolfgang Hackbusch:
On the Efficient Evaluation of Coalescence Integrals in Population Balance Models. Computing 78(2): 145-159 (2006) - 2005
- [j32]Steffen Börm, Wolfgang Hackbusch:
Hierarchical Quadrature for Singular Integrals. Computing 74(2): 75-100 (2005) - [j31]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems. Computing 74(2): 131-157 (2005) - [j30]Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov:
Hierarchical Kronecker tensor-product approximations. J. Num. Math. 13(2): 119-156 (2005) - [j29]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
Data-sparse approximation to a class of operator-valued functions. Math. Comput. 74(250): 681-708 (2005) - 2004
- [j28]Lars Grasedyck, Wolfgang Hackbusch, Sabine Le Borne:
Adaptive Geometrically Balanced Clustering of H-Matrices. Computing 73(1): 1-23 (2004) - [j27]Wolfgang Hackbusch, Boris N. Khoromskij, Ronald Kriemann:
Hierarchical Matrices Based on a Weak Admissibility Criterion. Computing 73(3): 207-243 (2004) - [j26]Wolfgang Dahmen, B. Faermann, Ivan G. Graham, Wolfgang Hackbusch, Stefan A. Sauter:
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Math. Comput. 73(247): 1107-1138 (2004) - [j25]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
Data-sparse approximation to the operator-valued functions of elliptic operator. Math. Comput. 73(247): 1297-1324 (2004) - 2003
- [j24]Lars Grasedyck, Wolfgang Hackbusch, Boris N. Khoromskij:
Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices. Computing 70(2): 121-165 (2003) - [j23]Lars Grasedyck, Wolfgang Hackbusch:
Construction and Arithmetics of H-Matrices. Computing 70(4): 295-334 (2003) - [j22]Mario Bebendorf, Wolfgang Hackbusch:
Existence of ℋ-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-coefficients. Numerische Mathematik 95(1): 1-28 (2003) - 2002
- [j21]Wolfgang Hackbusch:
Direct Integration of the Newton Potential over Cubes. Computing 68(3): 193-216 (2002) - [j20]Wolfgang Hackbusch, Steffen Börm:
Data-sparse Approximation by Adaptive H2-Matrices. Computing 69(1): 1-35 (2002) - [j19]Wolfgang Hackbusch, Boris N. Khoromskij:
Blended kernel approximation in the ℋ-matrix techniques. Numer. Linear Algebra Appl. 9(4): 281-304 (2002) - [j18]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
ℋ-Matrix approximation for the operator exponential with applications. Numerische Mathematik 92(1): 83-111 (2002) - 2001
- [j17]Wolfgang Hackbusch:
The Efficient Computation of Certain Determinants Arising in the Treatment of Schroedinger's Equations. Computing 67(1): 35-56 (2001) - [j16]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
ℋ-matrix approximation for elliptic solution operators in cylinder domains. J. Num. Math. 9(1): 25-58 (2001) - 2000
- [j15]Wolfgang Hackbusch, Boris N. Khoromskij:
A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems. Computing 64(1): 21-47 (2000) - [j14]Ivan G. Graham, Wolfgang Hackbusch, Stefan A. Sauter:
Discrete boundary element methods on general meshes in 3D. Numerische Mathematik 86(1): 103-137 (2000) - [j13]Ivan G. Graham, Wolfgang Hackbusch, Stefan A. Sauter:
Hybrid Galerkin boundary elements: theory and implementation. Numerische Mathematik 86(1): 139-172 (2000)
1990 – 1999
- 1999
- [j12]Wolfgang Hackbusch:
A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices. Computing 62(2): 89-108 (1999) - [j11]Dietrich Braess, Maksimillian Dryja, Wolfgang Hackbusch:
A Multigrid Method for Nonconforming FE-Discretisations with Application to Non-Matching Grids. Computing 63(1): 1-25 (1999) - 1998
- [j10]Wolfgang Hackbusch, J. U. Wappler:
Remarks on A Posteriori Error Estimation for Inaccurate Finite Element Solutions. Computing 60(2): 175-191 (1998) - [j9]Peter Bastian, Wolfgang Hackbusch, Gabriel Wittum:
Additive and Multiplicative Multi-Grid - A Comparison. Computing 60(4): 345-364 (1998) - 1997
- [j8]Wolfgang Hackbusch:
On the Feedback Vertex Set Problem for a Planar Graph. Computing 58(2): 129-156 (1997) - [j7]Wolfgang Hackbusch, Thomas Probst:
Downwind Gauß-Seidel Smoothing for Convection Dominated Problems. Numer. Linear Algebra Appl. 4(2): 85-102 (1997) - 1995
- [j6]Wolfgang Hackbusch:
A Note on Reusken's Lemma. Computing 55(2): 181-189 (1995) - 1994
- [j5]Wolfgang Hackbusch, Stefan A. Sauter:
On numerical cubatures of nearly singular surface integrals arising in BEM collocation. Computing 52(2): 139-159 (1994)
1980 – 1989
- 1989
- [j4]Wolfgang Hackbusch:
On first and second order box schemes. Computing 41(4): 277-296 (1989) - 1986
- [b2]Wolfgang Hackbusch:
Theorie und Numerik elliptischer Differentialgleichungen. Teubner Studienbücher, Teubner 1986, ISBN 978-3-519-02074-5, pp. 1-276 - 1985
- [b1]Wolfgang Hackbusch:
Multi-grid methods and applications. Springer series in computational mathematics 4, Springer 1985, ISBN 978-3-540-12761-1, pp. I-XVI, 1-377
1970 – 1979
- 1978
- [j3]Wolfgang Hackbusch:
On a method of characteristics for solving a hyperbolic equation of second order. Computing 20(1): 47-60 (1978) - [j2]Wolfgang Hackbusch:
A numerical method for solving parabolic equations with opposite orientations. Computing 20(3): 229-240 (1978) - [j1]Wolfgang Hackbusch:
On the multi-grid method applied to difference equations. Computing 20(4): 291-306 (1978)
Coauthor Index
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