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MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 229-241 (2002)
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# An introduction to hierarchical matrices

## Wolfgang Hackbusch, Lars Grasedyck, Steffen Börm

* Wolfgang Hackbusch*, Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany, e-mail: ` wh@mis.mpg.de`; * Lars Grasedyck*, Mathematisches Seminar Bereich 2, Universität Kiel, Hermann-Rodewald-Strasse 3, 24098 Kiel, Germany; * Steffen Börm*, Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany, e-mail: ` sbo@mis.mpg.de`

**Abstract:**
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. \endgraf The result of the approximation will be the so-called {hierarchical matrices} (or short \hbox {$\Cal {H}$-matrices}). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix multiplication, addition and inversion) can be performed in, up to logarithmic factors, optimal complexity.

**Keywords:** hierarchical matrices, data-sparse approximations, formatted matrix operations, fast solvers

**Classification (MSC2000):** 65F05, 65F30, 65F50, 65N50

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