Literature

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

Sabine Le Borne and Ronald Kriemann,
ℋ-FAINV: Hierarchically factored approximate inverse preconditioners,
Computing and Visualization in Science, Volume 17, Issue 3, pp 135-150,
2015.
Ronald Kriemann
ℋ-LU Factorization on Many-Core Systems,
Computing and Visualization in Science, 16, pp. 105-117,
2013.
Lars Grasedyck, Ronald Kriemann and Sabine Le Borne
Domain-decomposition based ℋ-LU preconditioning,
Numerische Mathematik 112, pp. 565-600,
2009.
Steffen Börm
Construction of data-sparse ℋ2-matrices by hierarchical compression,
SIAM J. Sci. Comput., 31:1820-1839,
2009.
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.
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.
Jelena Djokic,
Efficient update of hierarchical matrices in the case of adaptive discretisation schemes,
Ph.D. thesis, University of Leipzig,
2006.
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 Börm,
Adaptive variable-rank approximation of general dense matrices,
Preprint Nr. 114/2005, MPI Leipzig,
(submitted to "Numerische Mathematik").
Ronald Kriemann,
Parallele Algorithmen für 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.
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.
Lars Grasedyck, Wolfgang Hackbusch,
Construction and Arithmetics of ℋ-Matrices,
Computing 70, pp. 295-334
2003.
Wolfgang Hackbusch, Boris Khoromskij, Stefan Sauter,
On H2-matrices,
Lectures on Applied Mathematics, pp. 9-29,
2002.
Lars Grasedyck,
Theorie und Anwendungen Hierarchischer Matrizen,
Ph.D. Thesis, University of Kiel,
2001.
Wolfgang Hackbusch, Boris Khoromskij,
A sparse ℋ-matrix arithmetic. Part 2: Application to multi-dimensional problems,
Computing 64, pp. 21-47,
2000.
Wolfgang Hackbusch,
A sparse matrix arithmetic based on ℋ-matrices. Part I: Introduction to ℋ-matrices,
Computing 62, pp. 89-108,
1999.