An introduction to hierarchical matrices

Wolfgang Hackbusch, Lars Grasedyck, and Steffen Börm

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Submission date: 19. Dec. 2001
Pages: 12
published in: Mathematica bohemica, 127 (2002) 2, p. 229-241 
Bibtex
MSC-Numbers: 65F05, 65F30, 65F50, 65N50
Keywords and phrases: hierarchical matrices, data-sparse approximations, formatted matrix operations, fast solvers
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Abstract:
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.