{
  "id": "1012.2605",
  "version": "v1",
  "published": "2010-12-13T00:29:53.000Z",
  "updated": "2010-12-13T00:29:53.000Z",
  "title": "Rate of Convergence and Tractability of the Radial Function Approximation Problem",
  "authors": [
    "Gregory E. Fasshauer",
    "Fred J. Hickernell",
    "Henryk Woźniakowski"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "This article studies the problem of approximating functions belonging to a Hilbert space $H_d$ with an isotropic or anisotropic Gaussian reproducing kernel, $$ K_d(\\bx,\\bt) = \\exp\\left(-\\sum_{\\ell=1}^d\\gamma_\\ell^2(x_\\ell-t_\\ell)^2\\right) \\ \\ \\ \\mbox{for all}\\ \\ \\bx,\\bt\\in\\reals^d. $$ The isotropic case corresponds to using the same shape parameters for all coordinates, namely $\\gamma_\\ell=\\gamma>0$ for all $\\ell$, whereas the anisotropic case corresponds to varying shape parameters $\\gamma_\\ell$. We are especially interested in moderate to large $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-13T00:29:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D15",
      "68Q17",
      "41A25",
      "41A63"
    ],
    "keywords": [
      "radial function approximation problem",
      "tractability",
      "convergence",
      "anisotropic gaussian reproducing kernel",
      "anisotropic case corresponds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2605F"
    }
  }
}