Computing

, Volume 69, Issue 1, pp 1–35 | Cite as

Data-sparse Approximation by Adaptive ℋ2-Matrices

  • W. Hackbusch
  • S. 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: (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.

AMS Subject Classifications: 65F05, 65F30, 65F50, 65N38, 68P05, 45B05, 35C20.--> 
Keywords: Hierarchical matrices, nested bases, full matrices, fast matrix-vector multiplication, BEM, FEM. 

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • W. Hackbusch
    • 1
  • S. Börm
    • 1
  1. 1.Max-Planck-Institut, Mathematik in den Naturwissenschaften Inselstrasse 22–26 D-04103 Leipzig Germany e-mail: {wh, sbo}@mis.mpg.de www: http://www.mis.mpg.de/scicomp/DE

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