{
  "id": "0911.0410",
  "version": "v1",
  "published": "2009-11-02T22:06:13.000Z",
  "updated": "2009-11-02T22:06:13.000Z",
  "title": "Universality of Newton's method",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Convergence of the classical Newton's method and its DSM version for solving operator equations $F(u)=h$ is proved without any smoothness assumptions on $F'(u)$. It is proved that every solvable equation $F(u)=f$ can be solved by Newton's method if the initial approximation is sufficiently close to the solution and $||[F'(y)]^{-1}||\\leq m$, where $m>0$ is a constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-02T22:06:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47J05",
      "47J07",
      "58C15"
    ],
    "keywords": [
      "universality",
      "initial approximation",
      "classical newtons method",
      "smoothness assumptions",
      "dsm version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0410R"
    }
  }
}