NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS Numer. Linear Algebra Appl., 5, 253–274 (1998) Convergence Analysis of an Iterative Aggregation/dis- aggregation Method for Computing Stationary Probability Vectors of Stochastic Matrices Ivo Marek ∗ and Petr Mayer Katedra Numerick´e Matematiky, Na Matematicko – Fyzik´ aln´ ı fakultˇe, University Karlovy, Mal- ostransk´e n´ am. 25, 118 00 Praha 1, Czech Republic E-mail addresses: marek@ms.mff.cuni.cz and mayer@ms.mff.cuni.cz An aggregation/disaggregation iterative algorithm for computing stationary probability vectors of stochastic matrices is analysed. Two convergence results are presented. First, it is shown that fast, global convergence can be achieved provided that a sufficiently high number of relaxations is performed on the fine level. Second, local convergence is shown to take place with just one relaxation performed on the fine level. The convergence proofs are general and require no assumptions on the magnitude of off-diagonal elements (blocks). Furthermore, a relationship between the errors on the fine and on the coarse level is described. To illustrate the theory, the results of some numerical experiments are presented. © 1998 John Wiley & Sons, Ltd. KEY WORDS stochastic matrix, aggregation / disaggregation iterative methods 1. Introduction An aggregation/disaggregation iterative algorithm for computing stationary probability vec- tors of stochastic matrices is analysed. In fact, two convergence results are presented. The local convergence is shown to be guaranteed with any number t of relaxations made on the fine level, e.g., t = 1. In contrast to that, the global convergence is achieved only if a sufficient number of relaxations on the fine level is made. ∗ Correspondence to I. Marek, Katedra Numerick´ e Matematiky, Na Matematicko – Fyzik´ aln´ ı Fakultˇ e, Uni- versity Karlovy, Malostransk´ e n´ am. 25, 118 00 Praha 1, Czech Republic. Contract grant sponsor: Grant Agency of the Czech Republic; Contract grant number: 201/95/1486. Contract grant sponsor: Charles University Grant Agency; Contract grant number: 199/96. CCC 1070–5325/98/040253–22 $17.50 Received 10 September 1995 © 1998 John Wiley & Sons, Ltd. Revised 15 April 1997