{
  "id": "1310.1045",
  "version": "v3",
  "published": "2013-10-03T18:09:03.000Z",
  "updated": "2014-08-14T00:51:36.000Z",
  "title": "The divergence of the barycentric Pade approximants",
  "authors": [
    "Walter F. Mascarenhas"
  ],
  "comment": "Introducted a new section describing informally the proof of the main theorem",
  "categories": [
    "math.NA"
  ],
  "abstract": "We explain that, like the usual Pad\\'e approximants, the barycentric Pad\\'e approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P there exists a power series S, with arbitrarily small coefficients, such that the sequence of barycentric Pad\\'e approximants of P + S do not converge uniformly in any subset of the complex plane with a non-empty interior.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-14T00:51:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "barycentric pade approximants",
      "divergence",
      "usual pade approximants",
      "complex plane",
      "power series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.1045M"
    }
  }
}