LOCAL CONVERGENCE OF THE (EXACT AND INEXACT) ITERATIVE AGGREGATION METHOD FOR LINEAR-SYSTEMS AND MARKOV OPERATORS

The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) li near system is in turn solved iteratively; and to the problem of findi ng stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to the particular case o f stochastic matrices. Moreover, an argument is given which suggests w hy the iterative aggregation method works so well for nearly uncoupled Markov chains, as well as for Markov chains with other zero-nonzero s tructures.