On the superlinear convergence of Newton's method on Riemannian manifolds

Teles A. Fernandes, Orizon P. Ferreira, Yuan J. Yun

Published 2016-11-13Version 1

In this paper we study the Newton's method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of covariant derivative of the vector field at its singularity, we establish the well definition of the method in a suitable neighborhood of this singularity. Moreover, we also show that the generated sequence by Newton method converges for the solution with superlinear rate.