Expokit

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 94 articles , 1 standard article )

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  1. Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique: Efficient numerical integration of $N$th-order non-autonomous linear differential equations (2016)
  2. Borri, A.; Carravetta, F.; Mavelli, G.; Palumbo, P.: Block-tridiagonal state-space realization of chemical master equations: a tool to compute explicit solutions (2016)
  3. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  4. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: The Leja method revisited: backward error analysis for the matrix exponential (2016)
  5. Cao, Youfang; Terebus, Anna; Liang, Jie: State space truncation with quantified errors for accurate solutions to discrete chemical master equation (2016)
  6. Koskela, Antti; Jarlebring, Elias; Hochstenbach, Michiel E.: Krylov approximation of linear ODEs with polynomial parameterization (2016)
  7. López-García, M.: Stochastic descriptors in an SIR epidemic model for heterogeneous individuals in small networks (2016)
  8. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  9. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators (2016)
  10. Zhang, Rongpei; Zhu, Jiang; Loula, Abimael F.D.; Yu, Xijun: Operator splitting combined with positivity-preserving discontinuous Galerkin method for the chemotaxis model (2016)
  11. Bader, Philipp; Blanes, Sergio; Seydaoğlu, Muaz: The scaling, splitting, and squaring method for the exponential of perturbed matrices (2015)
  12. Blanes, Sergio: High order structure preserving explicit methods for solving linear-quadratic optimal control problems (2015)
  13. Deadman, Edvin: Estimating the condition number of $f(A)b$ (2015)
  14. House, Thomas: Algebraic moment closure for population dynamics on discrete structures (2015)
  15. Izaac, Josh A.; Wang, Jingbo B.: \itpyCTQW: a continuous-time quantum walk simulator on distributed memory computers (2015)
  16. Jia, Zhongxiao; Lv, Hui: A posteriori error estimates of Krylov subspace approximations to matrix functions (2015)
  17. Jimenez, J.C.; Carbonell, F.: Convergence rate of weak local linearization schemes for stochastic differential equations with additive noise (2015)
  18. Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart: Time integration of tensor trains (2015)
  19. Sidje, R.B.; Vo, H.D.: Solving the chemical master equation by a fast adaptive finite state projection based on the stochastic simulation algorithm (2015)
  20. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: Comparison of software for computing the action of the matrix exponential (2014)

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