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. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  2. Bormetti, G.; Callegaro, G.; Livieri, G.; Pallavicini, A.: A backward Monte Carlo approach to exotic option pricing (2018)
  3. Defez, Emilio; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Alonso, Pedro: A new efficient and accurate spline algorithm for the matrix exponential computation (2018)
  4. Hached, M.; Jbilou, K.: Numerical solutions to large-scale differential Lyapunov matrix equations (2018)
  5. Hashimoto, Yuka; Nodera, Takashi: Double-shift-invert Arnoldi method for computing the matrix exponential (2018)
  6. 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)
  7. Kressner, Daniel; Luce, Robert: Fast computation of the matrix exponential for a Toeplitz matrix (2018)
  8. Wu, Gang; Pang, Hong-Kui; Sun, Jiang-Li: A shifted block FOM algorithm with deflated restarting for matrix exponential computations (2018)
  9. Benner, Peter; Denißen, Jonas; Kohaupt, Ludwig: Trigonometric spline and spectral bounds for the solution of linear time-periodic systems (2017)
  10. Chekhovskoy, I. S.; Paasonen, V. I.; Shtyrina, O. V.; Fedoruk, M. P.: Numerical approaches to simulation of multi-core fibers (2017)
  11. Dilloo, Mehzabeen Jumanah; Tangman, Désiré Yannick: A high-order finite difference method for option valuation (2017)
  12. Hached, M.: A note on the Davison-Man method for Sylvester matrix equations (2017)
  13. Li, Yiqun; Wu, Boying; Leok, Melvin: Spectral variational integrators for semi-discrete Hamiltonian wave equations (2017)
  14. Lu, Dong; Zhang, Yong-Tao: Computational complexity study on Krylov integration factor WENO method for high spatial dimension convection-diffusion problems (2017)
  15. Miyajima, Shinya: Verified solutions of delay eigenvalue problems (2017)
  16. Nechepurenko, Yu. M.; Sadkane, M.: Computing humps of the matrix exponential (2017)
  17. Reisinger, Christoph; Süli, Endre; Whitley, Alan: A partial Fourier transform method for a class of hypoelliptic Kolmogorov equations (2017)
  18. Aprahamian, Mary; Higham, Nicholas J.: Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms (2016)
  19. Bini, D. A.; Dendievel, S.; Latouche, G.; Meini, B.: Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues (2016)
  20. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)

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