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An introduction to hierarchical matrices
Wolfgang Hackbusch, Lars Grasedyck and Steffen BörmAbstract
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 so-called hierarchical matrices (or short 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.
- Received:
- 19.12.01
- Published:
- 19.12.01
- MSC Codes:
- 65F05, 65F30, 65F50, 65N50
- Keywords:
- hierarchical matrices, data-sparse approximations, formatted matrix operations, fast solvers