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Inexact uniformization and GMRES methods for large Markov chains
Author(s) -
Sidje Roger B.
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.794
Subject(s) - uniformization (probability theory) , generalized minimal residual method , markov chain , residual , mathematics , transient (computer programming) , matrix (chemical analysis) , computer science , mathematical optimization , algorithm , markov model , markov property , statistics , materials science , composite material , operating system
SUMMARY Inexact algorithms allow certain operations (typically matrix–vector products or certain function evaluations) to be performed inexactly, either out of necessity or deliberately, in view of trading accuracy for speed. We review recent findings that show the impact of the inexact approach in the uniformization and generalized minimal residual (GMRES) methods when computing the transient, stationary, and cumulative solutions of realistic Markov chain problems of large size arising from computer systems and biochemical reactions. Copyright © 2011 John Wiley & Sons, Ltd.