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, Universitat Kiel, Hermann-Rodewald-Strasse 3, 24098 Kiel, Germany; Steffen Borm, 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. 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 (MSC 2000): 65F05, 65F30, 65F50, 65N50
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