{
  "id": "1611.04207",
  "version": "v1",
  "published": "2016-11-13T23:40:40.000Z",
  "updated": "2016-11-13T23:40:40.000Z",
  "title": "On the superlinear convergence of Newton's method on Riemannian manifolds",
  "authors": [
    "Teles A. Fernandes",
    "Orizon P. Ferreira",
    "Yuan J. Yun"
  ],
  "categories": [
    "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-13T23:40:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C30",
      "49M15",
      "65K05"
    ],
    "keywords": [
      "newtons method",
      "riemannian manifold",
      "superlinear convergence",
      "singularity",
      "newton method converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}