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# 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} }

- Published 2000 in Math. Comput.
DOI:10.1090/S0025-5718-00-01223-0

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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