{
  "id": "1808.01470",
  "version": "v1",
  "published": "2018-08-04T11:56:02.000Z",
  "updated": "2018-08-04T11:56:02.000Z",
  "title": "A note about EC-$(s,t)$-weak tractability of multivariate approximation with analytic Korobov kernels",
  "authors": [
    "Heping Wang"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "This note is devoted to discussing multivariate approximation of continuous functions on $[0,1]^d$ with analytic Korobov kernels in the worst and average case settings. We only consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We study EC-$(s, t)$-weak tractability under the absolute or normalized error criterion, and obtain necessary and sufficient conditions for $0<\\min(s,t)<1$ and $\\max(s,t)\\le 1$ in the worst case setting and for $s,t>0$ in the average case setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-04T11:56:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A63",
      "65D15",
      "65Y20"
    ],
    "keywords": [
      "analytic korobov kernels",
      "weak tractability",
      "average case setting",
      "arbitrary continuous linear functionals",
      "discussing multivariate approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}