Summary.
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) linear system is in turn solved iteratively; and to the problem of finding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to the particular case of stochastic matrices. Moreover, an argument is given which suggests why the iterative aggregation method works so well for nearly uncoupled Markov chains, as well as for Markov chains with other zero-nonzero structures.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received May 25, 1991/Revised version received February 23, 1994
Rights and permissions
About this article
Cite this article
Marek, I., Szyld, D. Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators . Numer. Math. 69, 61–82 (1994). https://doi.org/10.1007/s002110050080
Issue Date:
DOI: https://doi.org/10.1007/s002110050080