On H 2-Matrices

W. Hackbusch, B. Khoromskij and S. A. Sauter
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W. Hackbusch: Max-Planck-Institut Mathematik in den Naturwissenschaften
B. Khoromskij: Max-Planck-Institut Mathematik in den Naturwissenschaften
S. A. Sauter: Universität Zürich, Institut für Mathematik

A chapter in Lectures on Applied Mathematics, 2000, pp 9-29 from Springer

Abstract: Abstract 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.

Keywords: 65F05; 65F30; 65F50; 65N38; 68P05; 45B05; 35C20; Hierarchical matrices; hierarchical bases; full matrices; fast matrix-vector multiplication; BEM; FEM (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-3-642-59709-1_2

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