Manual
Literature

Documentation

Literature

In the following list a selection of references concerning 𝓗-matrices can be found.

2009

Lars Grasedyck, Ronald Kriemann and Sabine Le Borne
Domain-decomposition based 𝓗-LU preconditioning,
Numerische Mathematik 112, pp. 565-600,
2009.
Steffen BΓΆrm
Construction of data-sparse 𝓗2-matrices by hierarchical compression,
SIAM J. Sci. Comput., 31:1820-1839,
2009.

2008

Lars Grasedyck, Wolfgang Hackbusch and Ronald Kriemann
Performance of 𝓗-LU Preconditioning for Sparse Matrices,
Computational Methods in Applied Mathematics 8:4, pp. 336-349,
2008.

2007

Lars Grasedyck, Ronald Kriemann and Sabine Le Borne
Parallel blackbox 𝓗-LU preconditioning for elliptic boundary value problems,
Computing and Visualization in Science 11, pp. 273-291,
2007.

2006

Jelena Djokic,
Efficient update of hierarchical matrices in the case of adaptive discretisation schemes,
Ph.D. thesis, University of Leipzig,
2006.

2005

Lars Grasedyck, Ronald Kriemann and Sabine Le Borne,
Parallel Black Box Domain Decomposition Based 𝓗-LU Preconditioning,
Preprint Nr. 115/2005, MPI Leipzig,
(submitted to "Numerische Mathematik").
Steffen BΓΆrm,
Adaptive variable-rank approximation of general dense matrices,
Preprint Nr. 114/2005, MPI Leipzig,
(submitted to "Numerische Mathematik").
Ronald Kriemann,
Parallele Algorithmen fΓΌr 𝓗-Matrizen,
Ph.D. Thesis, University of Kiel
2005.
Sabine Le Borne, Lars Grasedyck and Ronald Kriemann,
Domain-decomposition based 𝓗-LU preconditioners,
Proceedings of the DD16, LNCSE.
Ronald Kriemann,
Parallel 𝓗-Matrix Arithmetics on Shared Memory Systems,
Computing 74, pp. 273-297,
2005.
Mario Bebendorf, Ronald Kriemann,
Fast Parallel Solution of Boundary Integral Equations and Related Problems,
Computing and Visualization in Sciences, 8/3-4, pp. 121-135,
2005.
Wolfgang Hackbusch, Boris N. Khoromskij, and Ronald Kriemann,
Direct Schur complement method by domain decomposition based on 𝓗-matrix approximation,
Computing and Visualization in Sciences, 8/3-4, pp. 179-188,
2005.

2004

Wolfgang Hackbusch, Boris N. Khoromskij, and Ronald Kriemann,
Direct Schur Complement Method by Hierarchical Matrix Techniques,
Domain Decomposition Methods in Science and Engineering, LNCSE, Vol. 40, pp. 581-589,
2004.
Wolfgang Hackbusch, Boris N. Khoromskij, and Ronald Kriemann,
Hierarchical Matrices based on a Weak Admissibility Criterion,
Computing 73, pp. 207-243,
2004.

2003

Lars Grasedyck, Wolfgang Hackbusch,
Construction and Arithmetics of 𝓗-Matrices,
Computing 70, pp. 295-334
2003.

2002

Wolfgang Hackbusch, Boris Khoromskij, Stefan Sauter,
On H2-matrices,
Lectures on Applied Mathematics, pp. 9-29,
2002.

2001

Lars Grasedyck,
Theorie und Anwendungen Hierarchischer Matrizen,
Ph.D. Thesis, University of Kiel,
2001.

2000

Wolfgang Hackbusch, Boris Khoromskij,
A sparse 𝓗-matrix arithmetic. Part 2: Application to multi-dimensional problems,
Computing 64, pp. 21-47,
2000.

1999

Wolfgang Hackbusch,
A sparse matrix arithmetic based on 𝓗-matrices. Part I: Introduction to 𝓗-matrices,
Computing 62, pp. 89-108,
1999.