{
  "id": "1610.02852",
  "version": "v1",
  "published": "2016-10-10T11:27:17.000Z",
  "updated": "2016-10-10T11:27:17.000Z",
  "title": "Truncation Dimension for Function Approximation",
  "authors": [
    "Peter Kritzer",
    "Friedrich Pillichshammer",
    "G. W. Wasilkowski"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number ${\\rm dim^{trnc}}(\\varepsilon)$ of variables. Here $\\varepsilon$ is the error demand and we refer to ${\\rm dim^{trnc}}(\\varepsilon)$ as the $\\varepsilon$-truncation dimension. We show that for sufficiently fast decaying product weights and modest error demand (up to about $\\varepsilon \\approx 10^{-5}$) the truncation dimension is surprisingly very small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-10T11:27:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "truncation dimension",
      "function approximation",
      "sufficiently fast decaying product weights",
      "modest error demand",
      "small number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}