{
  "id": "1710.00573",
  "version": "v1",
  "published": "2017-10-02T10:49:18.000Z",
  "updated": "2017-10-02T10:49:18.000Z",
  "title": "Tractability properties of the weighted star discrepancy of regular grids",
  "authors": [
    "Friedrich Pillichshammer"
  ],
  "categories": [
    "math.NA",
    "math.NT"
  ],
  "abstract": "In this paper we study tractability properties of the weighted star discrepancy with general coefficients of centered regular grids with different mesh-sizes. We give exact characterizations of the weight sequences $(\\gamma_j)_{j \\ge 1}$ such that the regular grid with different mesh-sizes achieves weak, uniform weak, quasi polynomial, polynomial or strong polynomial tractability for the $\\boldsymbol{\\gamma}$-weighted star discrepancy. For example, a necessary and sufficient condition such that the regular grid with different mesh-sizes achieves weak tractability for the $\\boldsymbol{\\gamma}$-weighted star discrepancy is $\\lim_{j \\rightarrow \\infty}j \\gamma_j=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-02T10:49:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "11K45",
      "65C05"
    ],
    "keywords": [
      "weighted star discrepancy",
      "regular grid",
      "mesh-sizes achieves weak tractability",
      "strong polynomial tractability",
      "study tractability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}