Abstract
We define the Newton iteration for solving the equation f(y) = 0, where f is a map from a Lie group to its
corresponding Lie algebra. Two versions Lie group. Both formulations reduce to the standard method in the
Euclidean case, and are related to existing algorithms on certain Riemannian manifolds. In particular, we show
that, under classical assumptions on f, the proposed method converges quadratically. We illustrate the
techniques by solving a fixed-point problem arising from the numerical integration of a Lie-type initial value
problem via implicit Euler.
This is joined work with B. Owren.
