Extending the applicability of Newton’s method on Lie groups

We use Newton’s method to approximate a zero of a mapping from a Lie group into its Lie algebra. Under the same computational cost as before, we show the semilocal convergence of Newton’s method with the following advantages over earlier works [55]: weaker sufficient convergence conditions, tighter error bounds on the distances involved and at least as precise information on the location of the solution. Numerical examples are also given for solving equations in cases not covered before.