Data-sparse Approximation by Adaptive ℋ2-Matrices
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.
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