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MiS Preprint
86/2001
Data-sparse approximation by adaptive ${\cal H^2}$-Matrices
Wolfgang Hackbusch and Steffen Börm
Abstract
A class of matrices (H2-matrices) has recently been introduced for storing discretisations of elliptic problems and integral operators from the BEM.
These matrices have the following properties:
They are sparse in the sense that only few data are needed for their representation.
The matrix-vector multiplication is of linear complexity.
In general, sums and products of these matrices are no longer in the same set, but after truncation to the H2-matrix format these operations are again of quasi-linear complexity.
We introduce the basic ideas of H- and H2-matrices and present an algorithm that adaptively computes approximations of general matrices in the latter format.
