Advertisement

Numerische Mathematik

, Volume 25, Issue 3, pp 291–295 | Cite as

Zur Konvergenz des symmetrischen Relaxationsverfahrens

  • G. Alefeld
  • R. S. Varga
Article

On the convergence of the symmetric SOR method

Summary

For the iterative solution of the matrix equationAx=b by means of the (point) symmetric SOR method (called the SSOR method), the basic convergence analysis of this iterative process has been developed in the literature only for the case whenA is Hermitian and positive definite. With the help of the theory of regular splittings, a more general convergence analysis of this iterative method is obtained, under the weaker assumption thatA is a nonsingularH-matrix.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. 1.
    Kulisch, U.: Über reguläre Zerlegungen von Matrizen und einige Anwendungen. Numer. Math.11, 444–449 (1968)Google Scholar
  2. 2.
    Ostrowski, A. M.: Über die Determinanten mit überwiegender Hauptdiagonale. Comment. Math. Helv.10, 69–96 (1937)Google Scholar
  3. 3.
    Varga, R. S.: Matrix Iterative Analysis. Engelwood Cliffs, N. J.: Pentrice Hall, Series in Automatic Computation (1962)Google Scholar
  4. 4.
    Young, D. M.: Iterative Solution of Large Linear Systems. Academic Press 1971Google Scholar
  5. 5.
    Young, D. M.: Second Degree Iterative Methods for the Solution of Large Linear Systems. Journal of Approx. Theory5, 137–148 (1972)Google Scholar
  6. 6.
    Young, D. M.: Convergence Properties of the Symmetric and Unsymmetric Successive Overrelaxation Methods and Related Methods. Mathematics of Computation24, 793–807 (1970)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • G. Alefeld
    • 1
  • R. S. Varga
    • 2
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheBundesrepublik Deutschland
  2. 2.Department of MathematicsKent State UniversityKentU. S. A.

Personalised recommendations