Geodesic
Convergence issues in the theory and practice of iterative aggregation/disaggregation methods
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 185-200
Iterative aggregation/disaggregation (IAD) methods for the computation of stationary probability vectors of large scale Markov chains form efficient practical analysis tools. However, their convergence theory is still not developed appropriately. Furthermore, as in other multilevel methods such as multigrid methods, the number of relaxations on the fine level of the IAD algorithms which is to be executed plays a very important role. To better understand these methods, in this paper we study some new concepts as well as their behavior and dependence on the parameters involved in aggregation algorithms, and establish some necessary and/or sufficient conditions for convergence. The theory developed offers a proof of convergence of IAD algorithms independent of whether the governing iteration matrix is primitive or cyclic as one of its main results. Another important result concerns a comparison of the rates of convergence of two IAD processes. Some examples documenting the diversity of behavior of IAD methods are given.
Classification : 15A15, 15A09, 15A23, 65F05
Keywords: stationary probability vector of Markov chain, iterative aggregation/disaggregation 
@article{ETNA_2009__35__a4,
     author = {Marek,  Ivo and Mayer,  Petr and Pultarov\'a,  Ivana},
     title = {Convergence issues in the theory and practice of iterative aggregation/disaggregation methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {185--200},
     year = {2009},
     volume = {35},
     zbl = {1190.65013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a4/}
}
TY  - JOUR
AU  - Marek,  Ivo
AU  - Mayer,  Petr
AU  - Pultarová,  Ivana
TI  - Convergence issues in the theory and practice of iterative aggregation/disaggregation methods
JO  - Electronic transactions on numerical analysis
PY  - 2009
SP  - 185
EP  - 200
VL  - 35
UR  - http://geodesic.mathdoc.fr/item/ETNA_2009__35__a4/
LA  - en
ID  - ETNA_2009__35__a4
ER  - 
%0 Journal Article
%A Marek,  Ivo
%A Mayer,  Petr
%A Pultarová,  Ivana
%T Convergence issues in the theory and practice of iterative aggregation/disaggregation methods
%J Electronic transactions on numerical analysis
%D 2009
%P 185-200
%V 35
%U http://geodesic.mathdoc.fr/item/ETNA_2009__35__a4/
%G en
%F ETNA_2009__35__a4
Marek,  Ivo; Mayer,  Petr; Pultarová,  Ivana. Convergence issues in the theory and practice of iterative aggregation/disaggregation methods. Electronic transactions on numerical analysis, Tome 35 (2009), pp. 185-200. http://geodesic.mathdoc.fr/item/ETNA_2009__35__a4/