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 140 articles , 1 standard article )

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  1. Lord, Gabriel J.; Tambue, Antoine: Stochastic exponential integrators for a finite element discretisation of SPDEs with additive noise (2019)
  2. Bormetti, G.; Callegaro, G.; Livieri, G.; Pallavicini, A.: A backward Monte Carlo approach to exotic option pricing (2018)
  3. Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)
  4. Ho, Lam Si Tung; Crawford, Forrest W.; Suchard, Marc A.: Direct likelihood-based inference for discretely observed stochastic compartmental models of infectious disease (2018)
  5. 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)
  6. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor Runge-Kutta methods (2018)
  7. Römer, Ulrich; Narayanamurthi, Mahesh; Sandu, Adrian: Solving parameter estimation problems with discrete adjoint exponential integrators (2018)
  8. Rostami, Minghao W.; Xue, Fei: Robust linear stability analysis and a new method for computing the action of the matrix exponential (2018)
  9. Wu, Gang; Pang, Hong-Kui; Sun, Jiang-Li: A shifted block FOM algorithm with deflated restarting for matrix exponential computations (2018)
  10. Zhang, Rongpei; Wang, Zheng; Liu, Jia; Liu, Luoman: A compact finite difference method for reaction-diffusion problems using compact integration factor methods in high spatial dimensions (2018)
  11. Ait-Haddou, Rachid: $q$-blossoming and Hermite-Padé approximants to the $q$-exponential function (2017)
  12. Einkemmer, Lukas; Tokman, Mayya; Loffeld, John: On the performance of exponential integrators for problems in magnetohydrodynamics (2017)
  13. 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)
  14. Nechepurenko, Yu. M.; Sadkane, M.: Computing humps of the matrix exponential (2017)
  15. Sadkane, Miloud; Sidje, Roger B.: An alternating maximization method for approximating the hump of the matrix exponential (2017)
  16. Yacouba, Simpore; Tambue, Antoine: Null controllability and numerical method for Crocco equation with incomplete data based on an exponential integrator and finite difference-finite element method (2017)
  17. Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique: Efficient numerical integration of $N$th-order non-autonomous linear differential equations (2016)
  18. Borri, A.; Carravetta, F.; Mavelli, G.; Palumbo, P.: Block-tridiagonal state-space realization of chemical master equations: a tool to compute explicit solutions (2016)
  19. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  20. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: The Leja method revisited: backward error analysis for the matrix exponential (2016)

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