# zbMATH — the first resource for mathematics

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

##### MSC:
 65F10 Iterative numerical methods for linear systems
Zbl 0225.65043
Full Text:
##### References:
 [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 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.