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An introduction to hierarchical matrices
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 229-241
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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 $\mathcal {H}$-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.
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 $\mathcal {H}$-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.
DOI : 10.21136/MB.2002.134156
Classification : 15A57, 65F05, 65F30, 65F50, 65N22, 65N38, 65N50, 65Y20
Keywords: hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers 
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Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen. An introduction to hierarchical matrices. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 229-241. doi: 10.21136/MB.2002.134156

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