{
  "id": "1705.04567",
  "version": "v1",
  "published": "2017-05-12T13:46:35.000Z",
  "updated": "2017-05-12T13:46:35.000Z",
  "title": "Optimal Monte Carlo Methods for $L^2$-Approximation",
  "authors": [
    "David Krieg"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling $n$ pieces of arbitrary linear information, including function values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-12T13:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A63",
      "65C05",
      "65D15",
      "65D30",
      "68Q25",
      "65Y20"
    ],
    "keywords": [
      "optimal monte carlo methods",
      "approximation",
      "function values",
      "construct monte carlo methods",
      "arbitrary linear information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}