Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ordinary differential equations with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

References in zbMATH (referenced in 126 articles , 1 standard article )

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  1. Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W.; Minin, Vladimir N.; Suchard, Marc A.: Birth/birth-death processes and their computable transition probabilities with biological applications (2018)
  2. Wu, Gang; Pang, Hong-Kui; Sun, Jiang-Li: A shifted block FOM algorithm with deflated restarting for matrix exponential computations (2018)
  3. Ait-Haddou, Rachid: $q$-blossoming and Hermite-Padé approximants to the $q$-exponential function (2017)
  4. Einkemmer, Lukas; Tokman, Mayya; Loffeld, John: On the performance of exponential integrators for problems in magnetohydrodynamics (2017)
  5. Fischer, Thomas M.: On the algorithm by Al-Mohy and Higham for computing the action of the matrix exponential: a posteriori roundoff error estimation (2017)
  6. Nechepurenko, Yu.M.; Sadkane, M.: Computing humps of the matrix exponential (2017)
  7. Sadkane, Miloud; Sidje, Roger B.: An alternating maximization method for approximating the hump of the matrix exponential (2017)
  8. Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique: Efficient numerical integration of $N$th-order non-autonomous linear differential equations (2016)
  9. Borri, A.; Carravetta, F.; Mavelli, G.; Palumbo, P.: Block-tridiagonal state-space realization of chemical master equations: a tool to compute explicit solutions (2016)
  10. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  11. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: The Leja method revisited: backward error analysis for the matrix exponential (2016)
  12. Cao, Youfang; Terebus, Anna; Liang, Jie: State space truncation with quantified errors for accurate solutions to discrete chemical master equation (2016)
  13. Cao, Youfang; Terebus, Anna; Liang, Jie: Accurate chemical master equation solution using multi-finite buffers (2016)
  14. Cong, Yuhao; Li, Dongping: Block Krylov subspace methods for approximating the linear combination of $\varphi$-functions arising in exponential integrators (2016)
  15. Drovandi, Christopher C.; Pettitt, Anthony N.; McCutchan, Roy A.: Exact and approximate Bayesian inference for low integer-valued time series models with intractable likelihoods (2016)
  16. Furtmaier, O.; Succi, S.; Mendoza, M.: Semi-spectral method for the Wigner equation (2016)
  17. Gaudreault, Stéphane; Pudykiewicz, Janusz A.: An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere (2016)
  18. Jagels, Carl; Mach, Thomas; Reichel, Lothar; Vandebril, Raf: Convergence rates for inverse-free rational approximation of matrix functions (2016)
  19. Koskela, Antti; Jarlebring, Elias; Hochstenbach, Michiel E.: Krylov approximation of linear ODEs with polynomial parameterization (2016)
  20. López-García, M.: Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks (2016)

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