Inexact uniformization and GMRES methods for large Markov chains

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.