{
  "id": "2304.14748",
  "version": "v1",
  "published": "2023-04-28T10:43:05.000Z",
  "updated": "2023-04-28T10:43:05.000Z",
  "title": "On the power of standard information for tractability for $L_\\infty$ approximation of periodic functions in the worst case setting",
  "authors": [
    "Jiaxin Geng",
    "Heping Wang"
  ],
  "comment": "25 pages. arXiv admin note: text overlap with arXiv:2101.05200, arXiv:2101.03665",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We study multivariate approximation of periodic function in the worst case setting with the error measured in the $L_\\infty$ norm. We consider algorithms that use standard information $\\Lambda^{\\rm std}$ consisting of function values or general linear information $\\Lambda^{\\rm all}$ consisting of arbitrary continuous linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability for $\\Lambda^{\\rm std}$ and $\\Lambda^{\\rm all}$ under the absolute or normalized error criterion, and show that the power of $\\Lambda^{\\rm std}$ is the same as the one of $\\Lambda^{\\rm all}$ for some notions of algebraic and exponential tractability. Our result can be applied to weighted Korobov spaces and Korobov spaces with exponential weight. This gives a special solution to Open problem 145 as posed by Novak and Wo\\'zniakowski (2012).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-28T10:43:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A63",
      "65C05",
      "65D15",
      "65Y20"
    ],
    "keywords": [
      "worst case setting",
      "standard information",
      "periodic function",
      "korobov spaces",
      "exponential tractability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}