On the superlinear convergence of Newton's method on Riemannian manifolds
Optimization and Control
2016-11-15 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1611.04207,
title = {On the superlinear convergence of Newton's method on Riemannian manifolds},
author = {Teles A. Fernandes and Orizon P. Ferreira and Yuan J. Yun},
journal= {arXiv preprint arXiv:1611.04207},
year = {2016}
}