{
  "id": "1703.07810",
  "version": "v1",
  "published": "2017-03-22T18:32:53.000Z",
  "updated": "2017-03-22T18:32:53.000Z",
  "title": "Solving underdetermined nonlinear equations by Newton-like method",
  "authors": [
    "Boris Polyak",
    "Andrey Tremba"
  ],
  "comment": "Authors' version",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "Newton method is one of the most powerful methods for finding solution of nonlinear equations. In its classical form it is applied for systems of $n$ equations with $n$ variables. However it can be modified for underdetermined equations (with $m<n$, $m$ being the number of equations). Theorems on solvability of such equations as well as conditions for convergence and rate of convergence of Newton-like methods are addressed in the paper. The results are applied to systems of quadratic equations, one-dimensional equations and inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T18:32:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M15",
      "65H10",
      "90C30",
      "G.1.5",
      "G.1.6"
    ],
    "keywords": [
      "solving underdetermined nonlinear equations",
      "newton-like method",
      "newton method",
      "convergence",
      "quadratic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}