{
  "id": "1805.09106",
  "version": "v1",
  "published": "2018-05-23T13:01:28.000Z",
  "updated": "2018-05-23T13:01:28.000Z",
  "title": "Transformed Rank-1 Lattices for high-dimensional approximation",
  "authors": [
    "Robert Nasdala",
    "Daniel Potts"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "This paper describes an extension of Fourier approximation methods for multivariate functions defined on bounded domains to unbounded ones via a multivariate change of coordinate mapping. In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials based on single and multiple reconstructing rank-1 lattices and make use of dimension incremental construction methods for sparse frequency sets. Various numerical tests confirm obtained theoretical results for the transformed methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T13:01:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05"
    ],
    "keywords": [
      "high-dimensional approximation",
      "dimension incremental construction methods",
      "multivariate trigonometric polynomials",
      "fourier approximation methods",
      "sparse frequency sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}