{
  "id": "1901.05752",
  "version": "v1",
  "published": "2019-01-17T12:17:39.000Z",
  "updated": "2019-01-17T12:17:39.000Z",
  "title": "Tractability of non-homogeneous tensor product problems in the worst case setting",
  "authors": [
    "Rong Guo",
    "Heping Wang"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "We study multivariate linear tensor product problems with some special properties in the worst case setting. We consider algorithms that use finitely many continuous linear functionals. We use a unified method to investigate tractability of the above multivariate problems, and obtain necessary and sufficient conditions for strong polynomial tractability, polynomial tractability, quasi-polynomial tractability, uniformly weak tractability, $(s,t)$-weak tractability, and weak tractability. Our results can apply to multivariate approximation problems with kernels corresponding to Euler kernels, Wiener kernels, Korobov kernels, Gaussian kernels, and analytic Korobov kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-17T12:17:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A63",
      "65D15",
      "65Y20"
    ],
    "keywords": [
      "non-homogeneous tensor product problems",
      "worst case setting",
      "weak tractability",
      "multivariate linear tensor product problems",
      "study multivariate linear tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}