A Block-GTH Algorithm for Finding the Stationary Vector of a Markov Chain

Grassman, Taksar, and Heyman have proposed an algorithm for computing the stationary vector of a Markov chain. Analysis by O'Cinneide confirmed the results of numerical experiments, proving that the GTH algorithm computes an approximation to the stationary vector with low relative error in each component. In this work, we develop a block form of the GTH algorithm, more efficient on high-performance architectures, and show that it too produces a vector with low relative error. We demonstrate the efficiency of the algorithm on vector processors and on workstations with hierarchical memory. 1. Introduction. We consider the problem of computing the steady state distribution of a finite, discrete time, irreducible Markov chain. Equivalently, we seek the left eigenvector r corresponding to the eigenvMue 1 of a stochastic matrix P: