A GRAPH BASED APPROACH TO THE CONVERGENCE OF ONELEVEL SCHWARZ ITERATIONS FOR SINGULAR M-MATRICESAND MARKOV CHAINS

摘要

We study the convergence of additive and multiplicative Schwarz iterations applied tosingular M-matrices and Markov chains. We do our investigations in order to solve consistent linearsystems or to calculate a probability distribution vector of a Markov chain. It turns out that for acertain set of equations we are able to prove convergence for both methods with a reliable degree offreedom concerning the overlap. These new convergence theorems are based on a graph theoreticalapproach and represent the main results of this paper. Other applications of the introduced theoryare also discussed.