On Latouche–Ramaswami's logarithmic reduction algorithm for quasi-birth-and-death processes

We consider Latouche–Ramaswami's logarithmic reduction algorithm for solving quasi-birth-and-death models. We shall present some theoretical properties concerning convergence of the algorithm and discuss numerical issues arising in finite precision implementations. In particular, we shall present a numerically more stable implementation. A rounding error analysis together with numerical examples are given to demonstrate the higher accuuracy achieved by the refined implementation.