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. Bocharov, G. A.; Nechepurenko, Yu. M.; Khristichenko, M. Yu.; Grebennikov, D. S.: Optimal perturbations of systems with delayed independent variables for control of dynamics of infectious diseases based on multicomponent actions (2021)
  2. Hashimoto, Yuka; Nodera, Takashi: Inexact rational Krylov method for evolution equations (2021)
  3. Muñoz-Matute, Judit; Pardo, David; Demkowicz, Leszek: A DPG-based time-marching scheme for linear hyperbolic problems (2021)
  4. Belyayev, Yuriy N.: Method for calculating multiwave scattering by layered anisotropic media (2020)
  5. Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D.: Exponential time differencing for the tracer equations appearing in primitive equation ocean models (2020)
  6. Caliari, Marco; Cassini, Fabio; Zivcovich, Franco: Approximation of the matrix exponential for matrices with a skinny field of values (2020)
  7. Diekmann, Odo; Scarabel, Francesca; Vermiglio, Rossana: Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures (2020)
  8. Frommer, Andreas; Hashemi, Behnam: Computing enclosures for the matrix exponential (2020)
  9. Hached, M.; Jbilou, K.: Numerical methods for differential linear matrix equations via Krylov subspace methods (2020)
  10. Liu, Shuang; Liu, Xinfeng: Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries (2020)
  11. Massei, Stefano; Robol, Leonardo; Kressner, Daniel: Hm-toolbox: MATLAB software for HODLR and HSS matrices (2020)
  12. Narayanamurthi, Mahesh; Sandu, Adrian: Efficient implementation of partitioned stiff exponential Runge-Kutta methods (2020)
  13. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  14. Fasi, Massimiliano: Optimality of the Paterson-Stockmeyer method for evaluating matrix polynomials and rational matrix functions (2019)
  15. Fasi, Massimiliano; Higham, Nicholas J.: An arbitrary precision scaling and squaring algorithm for the matrix exponential (2019)
  16. Krull, B. T.; Minion, M. L.: Parallel-in-Time Magnus integrators (2019)
  17. Liu, Yong; Gu, Chuanqing: A shift and invert reorthogonalization Arnoldi algorithm for solving the chemical master equation (2019)
  18. Liu, Yuan; Cheng, Yingda; Chen, Shanqin; Zhang, Yong-Tao: Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations (2019)
  19. Miyajima, Shinya: Verified computation of the matrix exponential (2019)
  20. Sastre, J.; Ibáñez, J.; Defez, E.: Boosting the computation of the matrix exponential (2019)

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