A class of matrices (H-matrices) has recently been introduced by one of the authors. 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 almost linear complexity, (iii) In general, sums and products of these matrices are no longer in the same set, but their truncations to the H-matrix format are again of almost linear complexity, (iv) The same statement holds for the inverse of an H-matrix.
The term “almost linear complexity” used above means that estimates are given by O(nlogα n). The logarithmic factor can be avoided by a further improvement, which is described in the present paper. We prove that the storage requirements and the cost of the matrix-vector multiplication is strictly linear in the dimension n, while still (full) system matrices of the boundary element method can be approximated up to the discretization error.
AMS Subject Classifications65F05 65F30 65F50 65N38 68P05 45B05 35C20
KeywordsHierarchical matrices hierarchical bases full matrices fast matrix-vector multiplication BEM FEM
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