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A Parallel Implementation of the Block-GTH Algorithm

In: Computations with Markov Chains

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  • Yuan-Jye Jason Wu

    (University of Maryland, Applied Mathematics Programs)

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.

Suggested Citation

  • Yuan-Jye Jason Wu, 1995. "A Parallel Implementation of the Block-GTH Algorithm," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 36, pages 597-598, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_36
    DOI: 10.1007/978-1-4615-2241-6_36
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