A convergence theorem for chaotic asynchronous relaxation (Q677117)

Chaotic asynchronous relaxation is discussed in relation to the iterative solution of the linear system \((I-B)x=d\), where \(I\) is the identity matrix. This method, which is a modification of that due to \textit{D. Chazan} and \textit{W. Miranker} [ibid. 2, 199-222 (1969; Zbl 0225.65043)], selects the order of updating components in an arbitrary manner and presents necessary and sufficient conditions for the convergence of the scheme. The difference between the methods is that the update is based on a prior state of the system rather than on prior substates.