|Start Page Number:||828|
|End Page Number:||843|
|Publication Date:||Jun 2017|
|Journal:||Journal of Optimization Theory and Applications|
|Authors:||Fernandes Teles, Ferreira Orizon, Yuan Jinyun|
In this paper, we study Newton’s method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of the covariant derivative of the vector field at its singularity, we show that Newton’s method is well defined in a suitable neighborhood of this singularity. Moreover, we show that the sequence generated by Newton’s method converges to the solution with superlinear rate.