{
  "id": "1512.00924",
  "version": "v1",
  "published": "2015-12-03T02:07:27.000Z",
  "updated": "2015-12-03T02:07:27.000Z",
  "title": "An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane",
  "authors": [
    "Difeng Cai"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "An explicit upper bound is derived for the modulus of divided difference for a function defined on a Jordan arc (or a Jordan curve) in the complex plane. As an immediate application, an error estimate for complex polynomial interpolation on a Jordan arc (or a Jordan curve) is given, which extends the well-known error estimate for polynomial interpolation on the unit interval. Moreover, this upper bound is independent of the parametrization of the curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T02:07:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D05",
      "65E05",
      "30E05",
      "65Q10"
    ],
    "keywords": [
      "explicit upper bound",
      "jordan arc",
      "complex plane",
      "divided difference",
      "jordan curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151200924C"
    }
  }
}