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MiS Preprint

Data-sparse approximation by adaptive -Matrices

Wolfgang Hackbusch and Steffen Börm


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:

  1. They are sparse in the sense that only few data are needed for their representation.
  2. The matrix-vector multiplication is of linear complexity.
  3. 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.

Nov 15, 2001
Nov 15, 2001
MSC Codes:
65F05, 65F30, 65F50, 65N38, 68P05, 45B05, 35C20
hierarchical matrices, nested bases, full matrices, fast matrix-vector multiplication, bem, fem

Related publications

2002 Repository Open Access
Wolfgang Hackbusch and Steffen Börm

Data-sparse approximation by adaptive \(\mathscr {H}^2\)-matrices

In: Computing, 69 (2002) 1, pp. 1-35