Data-sparse approximation by adaptive H2-matrices

Authors:
W. Hackbusch;S. Börm
Affiliations:
Max-Planck-Institut, Mathematik in den Naturwissenschaften Inselstrasse 22-26 D-04103 Leipzig Germany;Max-Planck-Institut, Mathematik in den Naturwissenschaften Inselstrasse 22-26 D-04103 Leipzig Germany
Venue:
Computing
Year:
2002

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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: (i) They are sparse in the sense that only few data are needed for their representation. (ii) The matrix-vector multiplication is of linear complexity. (iii) 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.