{
  "id": "1208.3068",
  "version": "v1",
  "published": "2012-08-15T09:29:13.000Z",
  "updated": "2012-08-15T09:29:13.000Z",
  "title": "Dependence on the Dimension for Complexity of Approximation of Random Fields (in Russian)",
  "authors": [
    "N. A. Serdyukova"
  ],
  "comment": "The original version in Russian was submitted on 15.01.2007 to Theor. Veroyatnost. i Primenen. and published as \"Zavisimost slozhnosti approximacii sluchajnyh polej ot rasmernosti\". The extended English translation is published in Theory Probab. Appl. (2010) 54:2, 272-284, arXiv: http://arxiv.org/abs/math/0701058",
  "journal": "Theor. Veroyatnost. i Primenen. (2009) 54:2, 256-270",
  "categories": [
    "math.PR",
    "math.SP"
  ],
  "abstract": "In the present paper a behavior of the \"average case\" approximation complexity for d-parametric random fields of tensor-type is studied. It was shown in [Lifshits and Tulyakova, 2006] that for a given approximation accuracy level the complexity of approximation increases exponentially, as d tends to infinity; that is the curse of dimensionality is observed. In this paper a technique allowing obtaining sharp asymptotic expressions for the approximation complexity is developed and such an expression is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-15T09:29:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A63",
      "60G60"
    ],
    "keywords": [
      "dependence",
      "approximation complexity",
      "obtaining sharp asymptotic expressions",
      "approximation accuracy level",
      "d-parametric random fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3068S"
    }
  }
}