{
  "id": "1709.03321",
  "version": "v1",
  "published": "2017-09-11T10:18:16.000Z",
  "updated": "2017-09-11T10:18:16.000Z",
  "title": "Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness",
  "authors": [
    "Glenn Byrenheid",
    "Robert J. Kunsch",
    "Van Kien Nguyen"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\\mathbb{T}^d$ into the space $L_{\\infty}(\\mathbb{T}^d)$ via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to $1/2$ in the main rate compared to the worst case approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-11T10:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A46",
      "41A63",
      "41A65",
      "65C05",
      "65J05"
    ],
    "keywords": [
      "periodic sobolev spaces",
      "monte carlo methods",
      "mixed smoothness",
      "uniform approximation",
      "nonlinear monte carlo approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}