Local convergence analysis of iterative aggregation–disaggregation methods with polynomial correction

Abstract

The paper introduces some new results on local convergence analysis of one class of iterative aggregation–disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix. We focus on methods, where the basic iteration on the fine level corresponds to a multiplication by a polynomial of order one with nonnegative coefficients in the original matrix. We show that this process is locally convergent for matrices with positive diagonals or when the coefficients of the polynomial are positive. On the other hand there are examples for which the process may diverge in a local sense for higher degree polynomials even if it converges for a polynomial of a lower degree for the same matrix.