A GRAPH BASED APPROACH TO THE CONVERGENCE OF ONE LEVEL SCHWARZ ITERATIONS FOR SINGULAR M-MATRICES AND MARKOV CHAINS.

We study the convergence of additive and multiplicative Schwarz iterations applied to singular M-matrices and Markov chains. We do our investigations in order to solve consistent linear systems or to calculate a probability distribution vector of a Markov chain. It turns out that for a certain set of equations we are able to prove convergence for both methods with a reliable degree of freedom concerning the overlap. These new convergence theorems are based on a graph theoretical approach and represent the main results of this paper. Other applications of the introduced theory are also discussed. [ABSTRACT FROM AUTHOR]