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On H 2-Matrices

In: Lectures on Applied Mathematics

Author

Listed:
  • 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)

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.

Suggested Citation

  • W. Hackbusch & B. Khoromskij & S. A. Sauter, 2000. "On H 2-Matrices," Springer Books, in: Hans-Joachim Bungartz & Ronald H. W. Hoppe & Christoph Zenger (ed.), Lectures on Applied Mathematics, pages 9-29, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59709-1_2
    DOI: 10.1007/978-3-642-59709-1_2
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