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 107 articles , 1 standard article )

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  1. 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)
  2. Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique: Efficient numerical integration of $N$th-order non-autonomous linear differential equations (2016)
  3. Borri, A.; Carravetta, F.; Mavelli, G.; Palumbo, P.: Block-tridiagonal state-space realization of chemical master equations: a tool to compute explicit solutions (2016)
  4. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  5. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: The Leja method revisited: backward error analysis for the matrix exponential (2016)
  6. Cao, Youfang; Terebus, Anna; Liang, Jie: Accurate chemical master equation solution using multi-finite buffers (2016)
  7. Cao, Youfang; Terebus, Anna; Liang, Jie: State space truncation with quantified errors for accurate solutions to discrete chemical master equation (2016)
  8. Furtmaier, O.; Succi, S.; Mendoza, M.: Semi-spectral method for the Wigner equation (2016)
  9. Gaudreault, Stéphane; Pudykiewicz, Janusz A.: An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere (2016)
  10. Koskela, Antti; Jarlebring, Elias; Hochstenbach, Michiel E.: Krylov approximation of linear ODEs with polynomial parameterization (2016)
  11. López-García, M.: Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks (2016)
  12. Pereira, Rodrigo M.; Garban, Christophe; Chevillard, Laurent: A dissipative random velocity field for fully developed fluid turbulence (2016)
  13. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  14. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators (2016)
  15. Zhang, Rongpei; Zhu, Jiang; Loula, Abimael F.D.; Yu, Xijun: Operator splitting combined with positivity-preserving discontinuous Galerkin method for the chemotaxis model (2016)
  16. Bader, Philipp; Blanes, Sergio; Seydaoğlu, Muaz: The scaling, splitting, and squaring method for the exponential of perturbed matrices (2015)
  17. Blanes, Sergio: High order structure preserving explicit methods for solving linear-quadratic optimal control problems (2015)
  18. Deadman, Edvin: Estimating the condition number of $f(A)b$ (2015)
  19. Dellar, Paul J.: Quantum lattice algorithms: similarities and connections to some classic finite difference algorithms (2015)
  20. House, Thomas: Algebraic moment closure for population dynamics on discrete structures (2015)

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