{
  "id": "1701.06778",
  "version": "v1",
  "published": "2017-01-24T09:20:55.000Z",
  "updated": "2017-01-24T09:20:55.000Z",
  "title": "Truncation Dimension for Linear Problems on Multivariate Function Spaces",
  "authors": [
    "Aicke Hinrichs",
    "Peter Kritzer",
    "Friedrich Pillichshammer",
    "G. W. Wasilkowski"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "The paper considers linear problems on weighted spaces of high-dimensional functions. The main questions addressed are: When is it possible to approximate the original function of very many variables by the same function; however with all but the first $k$ variables set to zero, so that the corresponding error is small? What is the truncation dimension, i.e., the smallest number $k=k(\\varepsilon)$ such that the corresponding error is bounded by a given error demand $\\varepsilon$? Surprisingly, $k(\\varepsilon)$ could be very small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-24T09:20:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65Y20",
      "65D30"
    ],
    "keywords": [
      "multivariate function spaces",
      "linear problems",
      "truncation dimension",
      "corresponding error",
      "high-dimensional functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}