Summary
We prove that if the matrixA has the structure which results from the so-called “red-black” ordering and ifA is anH-matrix then the symmetric SOR method (called the SSOR method) is convergent for 0<ω<2. In the special case thatA is even anM-matrix we show that the symmetric single-step method cannot be accelerated by the SSOR method. Symmetry of the matrixA is not assumed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alefeld, G., Varga, R.: Zur Konvergenz des symmetrischen Relaxationsverfahrens. Numer. Math.25, 291–295 (1976)
Niethammer, W.: Relaxation bei komplexen Matrizen. Math. Z.86, 34–40 (1964)
Ostrowski, A.M.: Über die Determinanten mit überwiegender Hauptdiagonale. Comment. Math. Helv.10, 69–96 (1937)
Varga, R.S.: Matrix iterative analysis. In: Series in Automatic Computation (Englewood Cliffs, N.J.) Prentice Hall (1962)
Varga, R.S.: On recurring theorems on diagonal dominance. LAA13, 1–9 (1976)
Young, D.M.: Iterative solution of large linear systems. Academic Press (1971)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alefeld, G. On the convergence of the symmetric SOR method for matrices with red-black ordering. Numer. Math. 39, 113–117 (1982). https://doi.org/10.1007/BF01399315
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01399315