{
  "id": "1803.06101",
  "version": "v1",
  "published": "2018-03-16T07:42:52.000Z",
  "updated": "2018-03-16T07:42:52.000Z",
  "title": "Tractability properties of the weighted star discrepancy of the Halton sequence",
  "authors": [
    "Aicke Hinrichs",
    "Friedrich Pillichshammer",
    "Shu Tezuka"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights $(\\gamma_j)_{j \\ge 1}$ under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires $\\sup_{d \\ge 1} \\max_{\\emptyset \\not= \\mathfrak{u} \\subseteq [d]} \\prod_{j \\in \\mathfrak{u}} (j \\gamma_j) < \\infty$. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-16T07:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "11K45",
      "65C05"
    ],
    "keywords": [
      "weighted star discrepancy",
      "tractability properties",
      "sequence achieves strong polynomial tractability",
      "halton sequence achieves strong polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}