Cyclic convergence of iterative methods in Markov modelling
Peter Schatte · Optimization · 1987
The stationary distribution of a continuous-time Markov chain satisfies a singular system of linear algebraic equations with the intensity matrix Aas coefficients. For solving such systems, iterative methods are considered, mainly the Jacob and the Gauss-Seidel methods. In order to enforce the convergence of these methods in every case, the notion of convergence is slightly generalized by averaging over a cycle of fixed length. Handy methods of finding a cycle of convergence are derived in which the directed graph of the Intensity matrix Ais considered. For the convergence of the Gauss-Seidel method the condition aij · aij≠0 for some i