Approximating the exponential from a Lie algebra to a Lie group

@article{Celledoni2000ApproximatingTE,
  title={Approximating the exponential from a Lie algebra to a Lie group},
  author={Elena Celledoni and Arieh Iserles},
  journal={Math. Comput.},
  year={2000},
  volume={69},
  pages={1457-1480}
}
Consider a differential equation y ′ = A(t, y)y, y(0) = y0 with y0 ∈ G and A : R+ × G → g, where g is a Lie algebra of the matricial Lie group G. Every B ∈ g can be mapped to G by the matrix exponential map exp (tB) with t ∈ R. Most numerical methods for solving ordinary differential equations (ODEs) on Lie groups are based on the idea of representing the approximation yn of the exact solution y(tn), tn ∈ R+, by means of exact exponentials of suitable elements of the Lie algebra, applied to the… CONTINUE READING
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