{
  "id": "1401.0638",
  "version": "v2",
  "published": "2014-01-03T12:54:10.000Z",
  "updated": "2014-07-17T01:20:59.000Z",
  "title": "Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities",
  "authors": [
    "Haiyong Wang"
  ],
  "comment": "The section 3 is revised",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we investigate the rate of convergence of Clenshaw-Curtis quadrature and its acceleration for functions with endpoint singularities in X^s, where X^s denotes the space of functions whose Chebyshev coefficients decay asymptotically as a_k = O(k^{-s-1}) for some positive s. For such unctions, we show that the convergence rate of (n + 1)-point Clenshaw-Curtis quadrature is O(n^{-s-2}). Furthermore, an asymptotic error expansion for Clenshaw-Curtis quadrature is presented which enables us to employ some extrapolation techniques to accelerate its convergence. Numerical examples are provided to confirm our analysis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-17T01:20:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clenshaw-curtis quadrature",
      "convergence rate",
      "endpoint singularities",
      "acceleration",
      "asymptotic error expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0638W"
    }
  }
}