{
  "id": "1706.02132",
  "version": "v1",
  "published": "2017-06-07T11:14:43.000Z",
  "updated": "2017-06-07T11:14:43.000Z",
  "title": "Newton correction methods for computing real eigenpairs of symmetric tensors",
  "authors": [
    "Ariel Jaffe",
    "Roi Weiss",
    "Boaz Nadler"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions for a real eigenpair to be a stable fixed point for our method, and prove that given a sufficiently close initial guess, the convergence rate is quadratic. Empirically, our method converges to a significantly larger number of eigenpairs compared to previously proposed iterative methods, and with enough random intializations typically finds all real eigenpairs. We conjecture that for a generic symmetric tensor, the sufficient conditions for local convergence of our Newton-based method hold simultaneously for all its real eigenpairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-07T11:14:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A69",
      "15A72",
      "15A18",
      "49M15"
    ],
    "keywords": [
      "newton correction methods",
      "computing real eigenpairs",
      "sufficient conditions",
      "random intializations typically finds",
      "generic symmetric tensor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}