A multi-level solution algorithm for steady-state Markov chains
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains
SIAM Journal on Scientific Computing
Stochastic Automata Networks and Near Complete Decomposability
SIAM Journal on Matrix Analysis and Applications
A Reordering for the PageRank Problem
SIAM Journal on Scientific Computing
Convergence Analysis of a PageRank Updating Algorithm by Langville and Meyer
SIAM Journal on Matrix Analysis and Applications
On the Convergence of a Class of Multilevel Methods for Large Sparse Markov Chains
SIAM Journal on Matrix Analysis and Applications
PageRank Computation, with Special Attention to Dangling Nodes
SIAM Journal on Matrix Analysis and Applications
Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking
SIAM Journal on Scientific Computing
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
NCDawareRank: a novel ranking method that exploits the decomposable structure of the web
Proceedings of the sixth ACM international conference on Web search and data mining
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This paper introduces an error propagation formula of a certain class of multi-level iterative aggregation-disaggregation (IAD) methods for numerical solutions of stationary probability vectors of discrete finite Markov chains. The formula can be used to investigate convergence by computing the spectral radius of the error propagation matrix for specific Markov chains. Numerical experiments indicate that the same type of the formula could be used for a wider class of the multi-level IAD methods. Using the formula we show that for given data there is no relation between convergence of two-level and of multi-level IAD methods.