On the comparisons of the multisplitting unsymmetric aor methods for M-matrices

This paper reveals the inner links between two known frameworks of multisplitting relaxation methods as completely as possible. By meticulously investigating the specific structures of these two frameworks, the asymptotic convergence rates as well as the monotone convergence rates of them are compared theoretically. This then definitely answers the question that which converges faster between these two frameworks of parallel matrix multisplitting relaxation methods from the standpoint of pure mathematics. At last, an example further confirms the correctness of the theoretical results.