Skip to main content
SpringerLink
Log in

Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

A variety of iterative methods considered in [3] are applied to linear algebraic systems of the formAu=b, where the matrixA is consistently ordered [12] and the iteration matrix of the Jacobi method is skew-symmetric. The related theory of convergence is developed and the optimum values of the involved parameters for each considered scheme are determined. It reveals that under the aforementioned assumptions the Extrapolated Successive Underrelaxation method attains a rate of convergence which is clearly superior over the Successive Underrelaxation method [5] when the Jacobi iteration matrix is non-singular.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ehrlich, L.W.: Coupled harmonic equations, SOR and Chebyshev acceleration. Math. Comput.26, 335–343 (1973)

    Google Scholar 

  2. Hadjidimos, A.: Accelerated overrelaxation method. Math. Comput.32, 149–157 (1978)

    Google Scholar 

  3. Missirlis, N.M., Evans, D.J.: On the convergence of some generalised preconditioned iterative methods. SIAM J. Numer. Anal.18, 591–596 (1981)

    Google Scholar 

  4. Niethammer, W.: Iterationsverfahren bei der konformen Abbildung. Computing2, 146–153 (1966)

    Google Scholar 

  5. Niethammer, W.: Über- und Unterrelaxation bei linearen Gleichungssystemen. Computing5, 303–311 (1970)

    Google Scholar 

  6. Niethammer, W.: On different splittings and the associated iteration methods. SIAM J. Numer. Anal.16, 186–200 (1979)

    Google Scholar 

  7. Sisler, M.: Über ein zweiparametriges Iterations-Verfahren. Aplikace Matematiky18, 325–332 (1973)

    Google Scholar 

  8. Sisler, M.: Über die optimierung eines zweiparametrigen Iterations-Verfahrens.Ibid20, 126–142 (1975)

    Google Scholar 

  9. Sisler, M.: Bemerkungen zur optimierung eines zweiparametrigen Iterations-Verfahrens.Ibid21, 213–320 (1976)

    Google Scholar 

  10. Späth, H.: The numerical calculation of high degree Lidstone splines with equidistant knots by block underrelaxation. Computing7, 65–74 (1971)

    Google Scholar 

  11. Varga, R.S.: Matrix Iterative Analysis. Englewood Cliffs, New Jersey: Prentice Hall 1962

    Google Scholar 

  12. Young, D.M.: Iterative solution of large linear systems. New York: Academic Press 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Athens, Panepistimiopolis, 15710, Athens, Greece

    Nikolaos M. Missirlis

Authors
  1. Nikolaos M. Missirlis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Missirlis, N.M. Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems. Numer. Math. 45, 447–458 (1984). https://doi.org/10.1007/BF01391419

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01391419

Subject Classifications

Search

Navigation