Data-sparse approximation by adaptive H2-matrices

doi:10.1007/s00607-002-1450-4

Data-sparse approximation by adaptive H2-matrices

2002-09-01

196

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AI

DOI：10.1007/s00607-002-1450-4

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A class of matrices (H-2-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 H-2-matrix format these operations are again of quasi-linear complexity. We introduce the basic ideas of H- and H-2-matrices and present an algorithm that adaptively computes approximations of general matrices in the latter format.

Keyword:

hierarchical matrices

nested bases

full matrices

fast matrix-vector multiplication

BEM

FEM

Data-sparse approximation by adaptive H2-matrices

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