Comparison of methods for evaluating functions of a matrix exponential

H. A. Ashi, L. J. Cummings, P. C. Matthews

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We compare six different categories of numerical methods for the evaluation of functions of the matrix exponential. These functions are required for exponential integrators, and are not straightforward to evaluate because they are highly susceptible to rounding errors when the matrix has small eigenvalues. The comparison takes into account both accuracy and computational time. A scaling and squaring algorithm and a diagonalisation algorithm are both found to be efficient.

Original languageEnglish (US)
Pages (from-to)468-486
Number of pages19
JournalApplied Numerical Mathematics
Issue number3-4
StatePublished - Mar 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


  • Exponential integrators
  • Exponential time differencing methods
  • Matrix exponential
  • Stiff differential equations


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