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. 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. Boito, Paola; Eidelman, Yuli; Gemignani, Luca: Computing the reciprocal of a (\phi)-function by rational approximation (2022)
  3. Li, Dongping; Yang, Siyu; Lan, Jiamei: Efficient and accurate computation for the (\varphi)-functions arising from exponential integrators (2022)
  4. Massei, Stefano; Robol, Leonardo: Mixed precision recursive block diagonalization for bivariate functions of matrices (2022)
  5. Nasr, Walid W.: Inventory systems with stochastic and batch demand: computational approaches (2022)
  6. Nechepurenko, Yuri M.; Zasko, Grigory V.: Constant upper bounds on the matrix exponential norm (2022)
  7. Areias, P.; Rosa, P. A. R.; Rabczuk, T.: Fully anisotropic hyperelasto-plasticity with exponential approximation by power series and scaling/squaring (2021)
  8. Benth, Fred Espen; Lavagnini, Silvia: Correlators of polynomial processes (2021)
  9. 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)
  10. Hashimoto, Yuka; Nodera, Takashi: Inexact rational Krylov method for evolution equations (2021)
  11. Lan, Rihui; Leng, Wei; Wang, Zhu; Ju, Lili; Gunzburger, Max: Parallel exponential time differencing methods for geophysical flow simulations (2021)
  12. Maset, Stefano: Relative error analysis of matrix exponential approximations for numerical integration (2021)
  13. Meier, Christian; Li, Lingfei; Zhang, Gongqiu: Markov chain approximation of one-dimensional sticky diffusions (2021)
  14. Muñoz-Matute, Judit; Pardo, David; Demkowicz, Leszek: A DPG-based time-marching scheme for linear hyperbolic problems (2021)
  15. Thuillier, Julien; Delouche, David; Fantini, Jacques; Kratz, Frédéric: Detection of integrity loss in networked control systems using an interval finite memory observer (2021)
  16. Wu, Feng; Zhang, Kailing; Zhu, Li; Hu, Jiayao: High-performance computation of the exponential of a large sparse matrix (2021)
  17. Belyayev, Yuriy N.: Method for calculating multiwave scattering by layered anisotropic media (2020)
  18. Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D.: Exponential time differencing for the tracer equations appearing in primitive equation ocean models (2020)
  19. Caliari, Marco; Cassini, Fabio; Zivcovich, Franco: Approximation of the matrix exponential for matrices with a skinny field of values (2020)
  20. Diekmann, Odo; Scarabel, Francesca; Vermiglio, Rossana: Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures (2020)

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