Periodic chaotic relaxation. (English) Zbl 0213.16306

The author generalizes some recent results of D. Chazan and W. Miranker [ibid. 2, 199–222 (1969; Zbl 0225.65043)] for relaxation methods applied to \(Ax=b\) using several processors.
In this paper \(A\) is taken to be positive definite. Two theorems establish sufficient conditions on the overrelaxation factor for convergence. A model problem is discussed in which the optimum rate of convergence in \(O(h^2)\) for several processors against \(O(h)\) for one.
Reviewer: J. D. P. Donnelly


65F10 Iterative numerical methods for linear systems


Zbl 0225.65043
Full Text: DOI


[1] Chazan, D.; Miranker, W., Chaotic relaxation, Linear Algebra, 2, 199-222 (1969) · Zbl 0225.65043
[2] Varga, R., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0133.08602
[3] Black, A. N.; Southwell, R. V., Relaxation methods applied to engineering problems, Proc. Roy. Soc., A164, 447-467 (1938) · JFM 64.0822.02
[4] Temple, G., The general theory of relaxation methods applied to linear systems, Proc. Roy. Soc., A169, 476-500 (1939) · Zbl 0020.24706
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