An introduction to hierarchical matrices. (English) Zbl 1007.65032

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.


65F30 Other matrix algorithms (MSC2010)
65N38 Boundary element methods for boundary value problems involving PDEs
15B57 Hermitian, skew-Hermitian, and related matrices
65F50 Computational methods for sparse matrices
65F05 Direct numerical methods for linear systems and matrix inversion
65Y20 Complexity and performance of numerical algorithms
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