Article
MSC:
15A57,
65F05,
65F30,
65F50,
65N22,
65N38,
65N50,
65Y20 | MR 1981528 | Zbl 1007.65032 | DOI: 10.21136/MB.2002.134156
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Keywords:
hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers
hierarchical matrices; data-sparse approximations; formatted matrix operations; fast solvers
Summary:
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.
References:
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