Numerische Mathematik

, Volume 45, Issue 3, pp 447–458 | Cite as

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

  • Nikolaos M. Missirlis
Article

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.

Subject Classifications

AMS(MOS): 65F10 CR: G.1.3 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ehrlich, L.W.: Coupled harmonic equations, SOR and Chebyshev acceleration. Math. Comput.26, 335–343 (1973)Google Scholar
  2. 2.
    Hadjidimos, A.: Accelerated overrelaxation method. Math. Comput.32, 149–157 (1978)Google Scholar
  3. 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. 4.
    Niethammer, W.: Iterationsverfahren bei der konformen Abbildung. Computing2, 146–153 (1966)Google Scholar
  5. 5.
    Niethammer, W.: Über- und Unterrelaxation bei linearen Gleichungssystemen. Computing5, 303–311 (1970)Google Scholar
  6. 6.
    Niethammer, W.: On different splittings and the associated iteration methods. SIAM J. Numer. Anal.16, 186–200 (1979)Google Scholar
  7. 7.
    Sisler, M.: Über ein zweiparametriges Iterations-Verfahren. Aplikace Matematiky18, 325–332 (1973)Google Scholar
  8. 8.
    Sisler, M.: Über die optimierung eines zweiparametrigen Iterations-Verfahrens.Ibid20, 126–142 (1975)Google Scholar
  9. 9.
    Sisler, M.: Bemerkungen zur optimierung eines zweiparametrigen Iterations-Verfahrens.Ibid21, 213–320 (1976)Google Scholar
  10. 10.
    Späth, H.: The numerical calculation of high degree Lidstone splines with equidistant knots by block underrelaxation. Computing7, 65–74 (1971)Google Scholar
  11. 11.
    Varga, R.S.: Matrix Iterative Analysis. Englewood Cliffs, New Jersey: Prentice Hall 1962Google Scholar
  12. 12.
    Young, D.M.: Iterative solution of large linear systems. New York: Academic Press 1971Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Nikolaos M. Missirlis
    • 1
  1. 1.Department of Applied MathematicsUniversity of AthensAthensGreece

Personalised recommendations