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An accelerated conjugate gradient algorithm to compute low-lying eigenvalues of sparse hermitian matrices

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High-Performance Computing and Networking (HPCN-Europe 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1067))

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Abstract

The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. The algorithm presented here is accelerated by a factor 4–8 by alternating CG searches with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. The algorithm is numerically very stable and can be parallelized in an efficient way.

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Author information

Authors and Affiliations

  1. Institut für Physik, Humboldt-Universität, Invalidenstraße 110, D-10099, Berlin, Germany

    Thomas Kalkreuter

  2. Department of Physics and Astronomy, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland

    Hubert Simma

Authors
  1. Thomas Kalkreuter
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  2. Hubert Simma
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Editor information

Heather Liddell Adrian Colbrook Bob Hertzberger Peter Sloot

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© 1996 Springer-Verlag Berlin Heidelberg

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Kalkreuter, T., Simma, H. (1996). An accelerated conjugate gradient algorithm to compute low-lying eigenvalues of sparse hermitian matrices. In: Liddell, H., Colbrook, A., Hertzberger, B., Sloot, P. (eds) High-Performance Computing and Networking. HPCN-Europe 1996. Lecture Notes in Computer Science, vol 1067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61142-8_673

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  • DOI: https://doi.org/10.1007/3-540-61142-8_673

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61142-4

  • Online ISBN: 978-3-540-49955-8

  • eBook Packages: Springer Book Archive

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