Incomplete WZ factorization as an alternative method of preconditioning for solving Markov chains

Authors:
Beata Bylina;Jarosław Bylina
Affiliations:
Department of Computer Science, Institute of Mathematics, Marie Curie-Sklodowska University, Lublin, Poland;Department of Computer Science, Institute of Mathematics, Marie Curie-Sklodowska University, Lublin, Poland
Venue:
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Year:
2007

Citing 4
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Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains

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Abstract

The purpose of the article is to present and evaluate usefulness of a new preconditioning technique (for the Gauss-Seidel algorithm), namely incomplete WZ factorization, for iterative solving of sparse and singular linear equations systems, which arise during modeling with Markov chains. The incomplete WZ factorization proposed here will be compared with the incomplete LU factorization in respect of amount of fill-in (newly created non-zeros) and in respect of the accuracy improvement of preconditioned algorithms in relation to not preconditioned ones. In the paper, the results of some numerical experiments will be presented, which were conducted for various matrices representing Markov chains. The experiments show that the incomplete WZ factorization can be a real alternative - because it is faster than incomplete LU factorization and the fill-in generated in the process is smaller (the output matrices are sparser).