The Scaling and Squaring Method for the Matrix Exponential Revisited

@article{Higham2009TheSA,
  title={The Scaling and Squaring Method for the Matrix Exponential Revisited},
  author={Nicholas John Higham},
  journal={Siam Review},
  year={2009},
  volume={51},
  pages={747-764}
}
  • N. Higham
  • Published 1 November 2009
  • Mathematics
  • Siam Review
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 Pade approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling. We give a new backward error analysis of the method (in exact arithmetic) that employs sharp bounds for the truncation errors… Expand

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