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Revisiting the matrix-free solution of Markov regenerative processes.
- Source :
-
Numerical Linear Algebra with Applications . Dec2011, Vol. 18 Issue 6, p1067-1083. 17p. - Publication Year :
- 2011
-
Abstract
- SUMMARY In this paper, we revisit the steady-state solution method for Markov Regenerative Processes (MRP) proposed in the work by German. This method solves the embedded Markov chain P of the MRP without storing the matrix P explicitly. We address three issues left open in German's Work: 1) the solution method is restricted to Power method; 2) it has been defined only for ergodic MRPs; and 3) no preconditioning is available to speed-up the computation. This paper discusses how to lift these limitations by extending the algorithm to preconditioned Krylov-subspace methods and by generalizing it to the non-ergodic case. An MRP-specific preconditioner is also proposed, which is built from a sparse approximation of the MRP matrix, computed via simulation. An experimental assessment of the proposed preconditioner is then provided. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10705325
- Volume :
- 18
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Numerical Linear Algebra with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 67480067
- Full Text :
- https://doi.org/10.1002/nla.819