An accelerated conjugate gradient algorithm to compute low-lying eigenvalues of sparse hermitian matrices | SpringerLink
Skip to main content
Springer Nature Link
Log in

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

  • Posters
  • Conference paper
  • First Online:
High-Performance Computing and Networking (HPCN-Europe 1996)

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

Included in the following conference series:

  • 157 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. G.H. Golub and C.F. v. Loan, Matrix computations, second edition, (The Johns Hopkins University Press, Baltimore, 1990).

    Google Scholar 

  2. J. Cullum and R.A. Willoughby, J. Comp. Phys. 44 (1981) 329.

    Google Scholar 

  3. T. Kalkreuter, hep-lat/9509071 (September 1995).

    Google Scholar 

  4. M. Geradin, J. Sound Vib. 19 (1971) 319; I. Fried, J. Sound Vib. 20 (1972) 333.

    Google Scholar 

  5. B. Bunk, K. Jansen, M. Lüscher, and H. Simma, internal DESY-report (1994).

    Google Scholar 

  6. T. Kalkreuter and H. Simma, Comp. Phys. Comm. 93 (1996) 33.

    Google Scholar 

  7. E. Polak, Comput. methods in optimization (Academic Press, New York, 1971).

    Google Scholar 

  8. W.H. Press, S.A. Teukolsky, W. T. Vetterling, and B.P. Flannery, Numerical recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).

    Google Scholar 

  9. H. Rutishauser, The Jacobi method for real symmetric matrices, in: J.H. Wilkinson and C. Reinsch, Linear Algebra (Springer-Verlag, Berlin, 1971).

    Google Scholar 

  10. M. Reed and B. Simon, Methods of modern mathematical physics, Vol. IV (Academic Press, New York, 1978).

    Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hubert Simma
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Heather Liddell Adrian Colbrook Bob Hertzberger Peter Sloot

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61142-4

  • Online ISBN: 978-3-540-49955-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation