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. ...

References in zbMATH (referenced in 95 articles , 1 standard article )

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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. Gaudreault, Stéphane; Pudykiewicz, Janusz A.: An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere (2016)
  6. Güttel, Stefan; Nakatsukasa, Yuji: Scaled and squared subdiagonal Padé approximation for the matrix exponential (2016)
  7. Jiang, Tian; Zhang, Yong-Tao: Krylov single-step implicit integration factor WENO methods for advection-diffusion-reaction equations (2016)
  8. Kaji, Shizuo; Ochiai, Hiroyuki: A concise parametrization of affine transformation (2016)
  9. Kavicharan, Mummaneni; Murthy, Nukala Suryanarayana; Rao, Nistala Bheema; Prathima, Addanki: Modeling and analysis of on-chip single and H-tree distributed RLC interconnects (2016)
  10. Piggott, M.J.; Solo, V.: Geometric Euler-Maruyama schemes for stochastic differential equations in $\mathrmSO(n)$ and $\mathrmSE(n)$ (2016)
  11. 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)
  12. Reichel, Lothar; Rodriguez, Giuseppe; Tang, Tunan: New block quadrature rules for the approximation of matrix functions (2016)
  13. Ruiz, P.; Sastre, J.; Ibáñez, J.; Defez, E.: High performance computing of the matrix exponential (2016)
  14. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators (2016)
  15. Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.: New algorithms for computing the matrix sine and cosine separately or simultaneously (2015)
  16. Bader, Philipp; Blanes, Sergio; Seydaoğlu, Muaz: The scaling, splitting, and squaring method for the exponential of perturbed matrices (2015)
  17. Dellar, Paul J.: Quantum lattice algorithms: similarities and connections to some classic finite difference algorithms (2015)
  18. Dorda, Antonius; Schürrer, Ferdinand: A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes (2015)
  19. Izaac, Josh A.; Wang, Jingbo B.: \itpyCTQW: a continuous-time quantum walk simulator on distributed memory computers (2015)
  20. Nguyen, Giang T.; Poloni, Federico: Componentwise accurate fluid queue computations using doubling algorithms (2015)

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