×

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.

MSC:

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
PDFBibTeX XMLCite
Full Text: EuDML