{
  "id": "1102.0055",
  "version": "v2",
  "published": "2011-02-01T01:51:23.000Z",
  "updated": "2011-02-12T20:43:26.000Z",
  "title": "Minimal Cubature rules and polynomial interpolation in two variables",
  "authors": [
    "Yuan Xu"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NA",
    "math.CA"
  ],
  "abstract": "Minimal cubature rules of degree $4n-1$ for the weight functions $$ W_{\\a,\\b,\\pm \\frac12}(x,y) = |x+y|^{2\\a+1} |x-y|^{2\\b+1} ((1-x^2)(1-y^2))^{\\pm \\frac12} $$ on $[-1,1]^2$ are constructed explicitly and are shown to be closed related to the Gaussian cubature rules in a domain bounded by two lines and a parabola. Lagrange interpolation polynomials on the nodes of these cubature rules are constructed and their Lebesgue constants are determined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-12T20:43:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A05",
      "65D05",
      "65D32"
    ],
    "keywords": [
      "minimal cubature rules",
      "polynomial interpolation",
      "gaussian cubature rules",
      "lagrange interpolation polynomials",
      "weight functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.0055X"
    }
  }
}