Periodic chaotic relaxation (Q2544887)

The author generalizes some recent results of \textit{D. Chazan} and \textit{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.