{
  "id": "2409.07810",
  "version": "v1",
  "published": "2024-09-12T07:39:59.000Z",
  "updated": "2024-09-12T07:39:59.000Z",
  "title": "Approximation of the Hilbert Transform on the unit circle",
  "authors": [
    "Luisa Fermo",
    "Valerio Loi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szeg\\\"o and anti-Szeg\\\"o quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy through their averaged results. Their computation involves a free parameter associated with the corresponding para-orthogonal polynomials. Here, it is suitably chosen to construct a Szeg\\\"o and anti-Szeg\\\"o formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T07:39:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D30",
      "42A10",
      "30E20",
      "32A55"
    ],
    "keywords": [
      "unit circle",
      "hilbert transform",
      "quadrature formulas",
      "maximum precision",
      "paper deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}