Extended semi-local convergence of Newton’s method on lie groups using restricted regions

Abstract

We extend the applicability of Newton’s method used to approximate a solution of a mapping involving Lie valued operators. Using our idea of the restricted convergence region, we locate a more precise set containing the Newton iterates leading to tighter majorizing sequences than before. This way and under the same computational cost as before, we show the semi-local convergence of Newton’s method with the following advantages over earlier works: weaker sufficient convergence criteria, tighter error bounds on the distances involved and at least as precise information on the location of the solution.