{
  "id": "1810.08505",
  "version": "v1",
  "published": "2018-10-19T13:54:57.000Z",
  "updated": "2018-10-19T13:54:57.000Z",
  "title": "Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces",
  "authors": [
    "Ken'ichiro Tanaka"
  ],
  "comment": "30 pages. The programs for the numerical computation in this article are available on https://github.com/KeTanakaN/mat_points_interp_rkhs",
  "categories": [
    "math.NA"
  ],
  "abstract": "We propose algorithms to take point sets for kernel-based interpolation of functions in reproducing kernel Hilbert spaces (RKHSs) by convex optimization. We consider the case of kernels with the Mercer expansion and propose an algorithm by deriving a second-order cone programming (SOCP) problem that yields $n$ points at one sitting for a given integer $n$. In addition, by modifying the SOCP problem slightly, we propose another sequential algorithm that adds an arbitrary number of new points in each step. Numerical experiments show that in several cases the proposed algorithms compete with the $P$-greedy algorithm, which is known to provide nearly optimal points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T13:54:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D05",
      "65D15",
      "41A05",
      "46E22"
    ],
    "keywords": [
      "reproducing kernel hilbert spaces",
      "convex optimization",
      "point sets",
      "interpolation",
      "generation"
    ],
    "tags": [
      "github project"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}