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 171 articles , 1 standard article )

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  1. Ackerer, Damien; Filipović, Damir: Linear credit risk models (2020)
  2. Bertaccini, D.; Durastante, F.: Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas (2020)
  3. Botchev, M. A.; Knizhnerman, L. A.: ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations (2020)
  4. Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D.: Exponential time differencing for the tracer equations appearing in primitive equation ocean models (2020)
  5. Ferreira, Orizon P.; Louzeiro, Mauricio S.; Prudente, Leandro F.: Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds (2020)
  6. Gao, Huadong; Ju, Lili; Duddu, Ravindra; Li, Hongwei: An efficient second-order linear scheme for the phase field model of corrosive dissolution (2020)
  7. Hoang, Thi-Thao-Phuong; Ju, Lili; Wang, Zhu: Nonoverlapping localized exponential time differencing methods for diffusion problems (2020)
  8. Jawecki, Tobias; Auzinger, Winfried; Koch, Othmar: Computable upper error bounds for Krylov approximations to matrix exponentials and associated (\varphi)-functions (2020)
  9. Jimenez, J. C.; de la Cruz, H.; De Maio, P. A.: Efficient computation of phi-functions in exponential integrators (2020)
  10. Narayanamurthi, Mahesh; Sandu, Adrian: Efficient implementation of partitioned stiff exponential Runge-Kutta methods (2020)
  11. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor two-step Runge-Kutta methods (2019)
  12. Liang, Shan; Zhang, Jian; Liu, Xia-Zhen; Hu, Xiao-Dong; Yuan, Wu: Domain decomposition based exponential time differencing method for fluid dynamics problems with smooth solutions (2019)
  13. Liu, Yong; Gu, Chuanqing: A shift and invert reorthogonalization Arnoldi algorithm for solving the chemical master equation (2019)
  14. Lord, Gabriel J.; Tambue, Antoine: Stochastic exponential integrators for a finite element discretisation of SPDEs with additive noise (2019)
  15. Narayanamurthi, Mahesh; Tranquilli, Paul; Sandu, Adrian; Tokman, Mayya: EPIRK-(W) and EPIRK-(K) time discretization methods (2019)
  16. Quiñones-Valles, Diego; Dolgov, Sergey; Savostyanov, Dmitry: Tensor product approach to quantum control (2019)
  17. Adam Glos, Jarosław Adam Miszczak, Mateusz Ostaszewski: QSWalk.jl: Julia package for quantum stochastic walks analysis (2018) arXiv
  18. Bhatt, H. P.; Khaliq, A. Q. M.; Wade, B. A.: Efficient Krylov-based exponential time differencing method in application to 3D advection-diffusion-reaction systems (2018)
  19. Bormetti, G.; Callegaro, G.; Livieri, G.; Pallavicini, A.: A backward Monte Carlo approach to exotic option pricing (2018)
  20. Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)

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