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. Aprahamian, Mary; Higham, Nicholas J.: Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms (2016)
  2. Bini, D.A.; Dendievel, S.; Latouche, G.; Meini, B.: Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues (2016)
  3. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  4. de la Hoz, Francisco; Vadillo, Fernando: Numerical simulations of time-dependent partial differential equations (2016)
  5. Güttel, Stefan; Nakatsukasa, Yuji: Scaled and squared subdiagonal Padé approximation for the matrix exponential (2016)
  6. Piggott, M.J.; Solo, V.: Geometric Euler-Maruyama schemes for stochastic differential equations in $\mathrmSO(n)$ and $\mathrmSE(n)$ (2016)
  7. Ramponi, Alessandro: On a transform method for the efficient computation of conditional V@R (and V@R) with application to loss models with jumps and stochastic volatility (2016)
  8. Reichel, Lothar; Rodriguez, Giuseppe; Tang, Tunan: New block quadrature rules for the approximation of matrix functions (2016)
  9. Ruiz, P.; Sastre, J.; Ibáñez, J.; Defez, E.: High performance computing of the matrix exponential (2016)
  10. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators (2016)
  11. Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.: New algorithms for computing the matrix sine and cosine separately or simultaneously (2015)
  12. Bader, Philipp; Blanes, Sergio; Seydaoğlu, Muaz: The scaling, splitting, and squaring method for the exponential of perturbed matrices (2015)
  13. Nguyen, Giang T.; Poloni, Federico: Componentwise accurate fluid queue computations using doubling algorithms (2015)
  14. Romm, Ya.E.: Computer-oriented stability analysis based on recurrent transformation of difference solutions of ordinary differential equations (2015)
  15. Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P.: New scaling-squaring Taylor algorithms for computing the matrix exponential (2015)
  16. Wang, Chengshan; Fu, Xiaopeng; Li, Peng; Wu, Jianzhong: Accurate dense output formula for exponential integrators using the scaling and squaring method (2015)
  17. Aprahamian, Mary; Higham, Nicholas J.: The matrix unwinding function, with an application to computing the matrix exponential (2014)
  18. Fischer, Thomas M.: On the stability of some algorithms for computing the action of the matrix exponential (2014)
  19. Jimenez, J.C.; Sotolongo, A.; Sanchez-Bornot, J.M.: Locally linearized Runge Kutta method of Dormand and Prince (2014)
  20. Mazzucco, Marco: A reduced-order matrices fitting scheme with log-Euclidean metrics for fast approximation of dynamic response of parametric structural systems (2014)

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