DagSemProc.07071.7.pdf
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Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices
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Dagstuhl Seminar Proceedings, Volume 7071
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-06-28
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Ivo Marek, Ivana Pultarová, and Petr Mayer. Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07071.7
Abstract
Iterative aggregation/disaggregation methods (IAD) belong to competitive tools for computation the characteristics of Markov chains as shown in some publications devoted to testing and comparing various methods designed to this purpose. According to Dayar T., Stewart W.J., ``Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains,'' SIAM J. Sci. Comput., Vol.21, No. 5, 1691-1705 (2000), the IAD methods are effective in particular when applied to large ill posed problems. One of the purposes of this paper is to contribute to a possible explanation of this fact. The novelty may consist of the fact that the IAD algorithms do converge independently of whether the iteration matrix of the corresponding process is primitive or not. Some numerical tests are presented and possible applications mentioned; e.g. computing the PageRank.
Subject Classification
Keywords
- Iterative aggregation methods
- stochastic matrix
- stationary probability vector
- Markov chains
- cyclic iteration matrix
- Google matrix
- PageRank.
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