{
  "id": "2101.09501",
  "version": "v1",
  "published": "2021-01-23T13:43:26.000Z",
  "updated": "2021-01-23T13:43:26.000Z",
  "title": "Exactness of quadrature formulas",
  "authors": [
    "Lloyd N. Trefethen"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature. Three further examples are mentioned more briefly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-23T13:43:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A55",
      "65D32"
    ],
    "keywords": [
      "quadrature formulas",
      "standard design principle",
      "gauss-hermite quadrature",
      "principle fails",
      "actual behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}