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 198 articles , 1 standard article )

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  1. Bader, Philipp; Blanes, Sergio; Casas, Fernando; Seydaoğlu, Muaz: An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation (2022)
  2. Jawecki, Tobias: A study of defect-based error estimates for the Krylov approximation of (\varphi)-functions (2022)
  3. Li, Dongping; Yang, Siyu; Lan, Jiamei: Efficient and accurate computation for the (\varphi)-functions arising from exponential integrators (2022)
  4. Botchev, M. A.: An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices (2021)
  5. Botchev, Mike A.; Knizhnerman, Leonid; Tyrtyshnikov, Eugene E.: Residual and restarting in Krylov subspace evaluation of the (\varphi) function (2021)
  6. Burrage, Kevin; Burrage, Pamela; Macnamara, Shev: Localization and pseudospectra of twisted Toeplitz matrices with applications to ion channels (2021)
  7. Chow, Kevin; Ruuth, Steven J.: Linearly stabilized schemes for the time integration of stiff nonlinear PDEs (2021)
  8. Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua: Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes (2021)
  9. Kang, Shinhoo; Bui-Thanh, Tan: A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations (2021)
  10. Lan, Rihui; Leng, Wei; Wang, Zhu; Ju, Lili; Gunzburger, Max: Parallel exponential time differencing methods for geophysical flow simulations (2021)
  11. Li, Dongping; Zhang, Xiuying; Liu, Renyun: Exponential integrators for large-scale stiff Riccati differential equations (2021)
  12. Meng, Xucheng; Hoang, Thi-Thao-phuong; Wang, Zhu; Ju, Lili: Localized exponential time differencing method for shallow water equations: algorithms and numerical study (2021)
  13. Naranjo-Noda, F. S.; Jimenez, J. C.: Locally linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems (2021)
  14. Narayanamurthi, Mahesh; Sandu, Adrian: Partitioned exponential methods for coupled multiphysics systems (2021)
  15. Patané, Giuseppe: Spectrum-free and meshless solvers of parabolic PDEs (2021)
  16. Seydaoğlu, Muaz; Bader, Philipp; Blanes, Sergio; Casas, Fernando: Computing the matrix sine and cosine simultaneously with a reduced number of products (2021)
  17. Wu, Feng; Zhang, Kailing; Zhu, Li; Hu, Jiayao: High-performance computation of the exponential of a large sparse matrix (2021)
  18. Yang, L. Minah; Grooms, Ian; Julien, Keith A.: The fidelity of exponential and IMEX integrators for wave turbulence: introduction of a new near-minimax integrating factor scheme (2021)
  19. Ackerer, Damien; Filipović, Damir: Linear credit risk models (2020)
  20. Bertaccini, D.; Durastante, F.: Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas (2020)

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