The scaling and squaring method for the matrix exponential revisited. The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in the MATLAB function expm. The method scales the matrix by a power of 2 to reduce the norm to order 1, computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling. ...

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  1. Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D.: Exponential time differencing for the tracer equations appearing in primitive equation ocean models (2020)
  2. Hached, M.; Jbilou, K.: Numerical methods for differential linear matrix equations via Krylov subspace methods (2020)
  3. Liu, Shuang; Liu, Xinfeng: Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries (2020)
  4. Massei, Stefano; Robol, Leonardo; Kressner, Daniel: Hm-toolbox: MATLAB software for HODLR and HSS matrices (2020)
  5. Narayanamurthi, Mahesh; Sandu, Adrian: Efficient implementation of partitioned stiff exponential Runge-Kutta methods (2020)
  6. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  7. Fasi, Massimiliano: Optimality of the Paterson-Stockmeyer method for evaluating matrix polynomials and rational matrix functions (2019)
  8. Fasi, Massimiliano; Higham, Nicholas J.: An arbitrary precision scaling and squaring algorithm for the matrix exponential (2019)
  9. Krull, B. T.; Minion, M. L.: Parallel-in-Time Magnus integrators (2019)
  10. Liu, Yong; Gu, Chuanqing: A shift and invert reorthogonalization Arnoldi algorithm for solving the chemical master equation (2019)
  11. Miyajima, Shinya: Verified computation of the matrix exponential (2019)
  12. Sastre, J.; Ibáñez, J.; Defez, E.: Boosting the computation of the matrix exponential (2019)
  13. Zhu, Xiaojing; Duan, Chunyan: On matrix exponentials and their approximations related to optimization on the Stiefel manifold (2019)
  14. 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)
  15. Bormetti, G.; Callegaro, G.; Livieri, G.; Pallavicini, A.: A backward Monte Carlo approach to exotic option pricing (2018)
  16. Defez, Emilio; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Alonso, Pedro: A new efficient and accurate spline algorithm for the matrix exponential computation (2018)
  17. Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya: KIOPS: a fast adaptive Krylov subspace solver for exponential integrators (2018)
  18. Hached, M.; Jbilou, K.: Numerical solutions to large-scale differential Lyapunov matrix equations (2018)
  19. Hashimoto, Yuka; Nodera, Takashi: Double-shift-invert Arnoldi method for computing the matrix exponential (2018)
  20. Heiberg, Thomas; Kriener, Birgit; Tetzlaff, Tom; Einevoll, Gaute T.; Plesser, Hans E.: Firing-rate models for neurons with a broad repertoire of spiking behaviors (2018)

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