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Summary: Numer. Math. 26,409--4-19 (1976)
@ by Springer-Verlag 1976
Zur Konvergenz des Peaceman-Rachford- Verfahrens
G.Alefeld
Received November 13,1975
On the Convergence of the Peaceman-Rachford Iterative Method
Summary. In this paper we prove some results concerning the convergence of
the Peaceman-Rachford iterative method. The main result covers both the stationary
and the instationary case. No use is made of the so called commutativity condition
which often was used in the literature in the instationary case. In proving the results
of this paper it is made use of the theory of regular splittings which was introduced by
RS. Varga. Finally it is demonstrated how the results can be applied to discrete ver-
sions of elliptic boundary value problems. .
1.
Gegeben sei ein lineares Gleichungssystem
Ax=b.
Die Matrix A sei zerlegt in die Summe
A=H+V
zweier Matrizen H und V. Zur Auflösung des gegebenen Gleichungssystems be-
trachten wir das Verfahren
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