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On H 2-Matrices

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Lectures on Applied Mathematics

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.

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References

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Dedicated to Professor Karl-Heinz Hoffmann on the ocasion of his 60th birthday

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© 2000 Springer-Verlag Berlin Heidelberg

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Hackbusch, W., Khoromskij, B., Sauter, S.A. (2000). On H 2-Matrices. In: Bungartz, HJ., Hoppe, R.H.W., Zenger, C. (eds) Lectures on Applied Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59709-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-59709-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64094-0

  • Online ISBN: 978-3-642-59709-1

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