We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
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.
