A Parallel Implementation of the Block-GTH Algorithm

Yuan-Jye Jason Wu
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Yuan-Jye Jason Wu: University of Maryland, Applied Mathematics Programs

Chapter 36 in Computations with Markov Chains, 1995, pp 597-598 from Springer

Abstract: Extended Abstract Finding the stationary distribution of a finite-state, discrete time, irreducible Markov chain is equivalent to seeking the left eigenvector corresponding to the eigenvalue 1 of a transition matrix P of order n. Grassmann, Taksar and Heyman [1] introduced a direct algorithm, the GTH algorithm, to find the steady-state vector π. Later O’Cinneide [2] showed that the computed vector π has low componentwise relative error. In order to reach high performance over a large class of computers, O’Leary and Wu [3] developed a block form algorithm, the block-GTH algorithm, and successfully demonstrated the efficiency of the algorithm on vector pipeline machines and on workstations with cache memory.

Date: 1995
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DOI: 10.1007/978-1-4615-2241-6_36

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