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Implementation of variable parameters in the Krylov-based finite state projection for solving the chemical master equation. (English) Zbl 1411.65070
Summary: 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.

65F60 Numerical computation of matrix exponential and similar matrix functions
65L05 Numerical methods for initial value problems
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Full Text: DOI
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