Computing the exponential in a Lie algebra

Arieh Iserles (Cambridge)

In this talk we consider the problem of computing an exponential of an element in a Lie algebra, so that the outcome resides in the underlying Lie group. Putting together an approach, due to Munthe-Kaas, Quispel and Zanna, of decomposing the algebra into a direct sum of triple Lie systems, together with ideas from numerical linear algebra, we devise an approximation algorithm which is substantially cheaper than the standard computational algorithms for the matrix exponential (which fail to produce a solution in the Lie group).