{
  "id": "1701.02910",
  "version": "v1",
  "published": "2017-01-11T10:06:28.000Z",
  "updated": "2017-01-11T10:06:28.000Z",
  "title": "Tractability of $\\mathbb{L}_2$-approximation in hybrid function spaces",
  "authors": [
    "Peter Kritzer",
    "Helene Laimer",
    "Friedrich Pillichshammer"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider multivariate $\\mathbb{L}_2$-approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worst-case error $e^{\\mathbb{L}_2-\\mathrm{app},\\Lambda}(N,d)$ of all algorithms that use $N$ information evaluations from the class $\\Lambda$ in the $d$-dimensional case. The two classes $\\Lambda$ considered in this paper are the class $\\Lambda^{{\\rm all}}$ consisting of all linear functionals and the class $\\Lambda^{{\\rm std}}$ consisting only of function evaluations. The focus lies on the dependence of $e^{\\mathbb{L}_2-\\mathrm{app},\\Lambda}(N,d)$ on the dimension $d$. The main results are conditions for weak, polynomial, and strong polynomial tractability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-11T10:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A63",
      "65D15",
      "65Y20"
    ],
    "keywords": [
      "hybrid function spaces",
      "approximation",
      "minimal worst-case error",
      "strong polynomial tractability",
      "reproducing kernel hilbert spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}