{
  "id": "1211.0871",
  "version": "v2",
  "published": "2012-11-05T14:18:14.000Z",
  "updated": "2013-04-16T11:42:36.000Z",
  "title": "The Curse of Dimensionality for Numerical Integration of Smooth Functions",
  "authors": [
    "Aicke Hinrichs",
    "Erich Novak",
    "Mario Ullrich",
    "Henryk Wozniakowski"
  ],
  "comment": "15 pages, minor revision",
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove the curse of dimensionality for multivariate integration of C^r functions: The number of needed function values to achieve an error \\epsilon\\ is larger than c_r (1+\\gamma)^d for \\epsilon\\le \\epsilon_0, where c_r,\\gamma>0 and d is the dimension. The proofs are based on volume estimates for r=1 together with smoothing by convolution. This allows us to obtain smooth fooling functions for r>1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-16T11:42:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D30",
      "65Y20",
      "41A63",
      "41A55"
    ],
    "keywords": [
      "smooth functions",
      "numerical integration",
      "dimensionality",
      "smooth fooling functions",
      "multivariate integration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.0871H"
    }
  }
}