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arXiv · 1611.04207

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

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

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Teles A. Fernandes, Orizon P. Ferreira, Yuan J. Yun. 2016-11-13. On the superlinear convergence of Newton's method on Riemannian manifolds. https://arxiv.org/abs/1611.04207

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