A direct projection method for Markov chains

A direct method based on oblique projections is adapted to compute the stationary distribution vector of a finite Markov chain. The algorithm can also be used to compute the group inverse of the corresponding generator matrix. It is shown how to update the stationary vector and other quantities of interest when one row of the transition probability matrix is modified. A GTH-like variant that appears to compute the stationary probabilities to high relative accuracy is developed. © 2004 Elsevier Inc. All rights reserved