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Implementation of variable parameters in the Krylov-based finite state projection for solving the chemical master equation

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  • Vo, H.D.
  • Sidje, R.B.

Abstract

The finite state projection (FSP) algorithm is a reduction method for solving the chemical master equation (CME). The Krylov-FSP improved on the original FSP by using an embedded scheme where the action of the matrix exponential is evaluated by the Krylov subspace method of Expokit for greater efficiency. There are parameters that impact the method, such as the stepsize that must be controlled to ensure the accuracy of the computed matrix exponentials, or to ensure the accuracy of the FSP. Other parameters include the dimension of the Krylov basis, or even the extent of reachability when expanding the FSP. In this work, we incorporate adaptive strategies to automatically vary these parameters. Numerical experiments comparing the resulting variants are reported, showing how certain choices perform better than others.

Suggested Citation

  • Vo, H.D. & Sidje, R.B., 2017. "Implementation of variable parameters in the Krylov-based finite state projection for solving the chemical master equation," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 334-344.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:334-344
    DOI: 10.1016/j.amc.2016.08.013
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    References listed on IDEAS

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    1. Sidje, Roger B. & Stewart, William J., 1999. "A numerical study of large sparse matrix exponentials arising in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 345-368, January.
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    Cited by:

    1. Liu, Yong & Gu, Chuanqing, 2019. "A shift and invert reorthogonalization Arnoldi algorithm for solving the chemical master equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 1-13.

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