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On the superlinear convergence of Newton's method on Riemannian manifolds (1611.04207v1)
Published 13 Nov 2016 in math.OC
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.