{
  "id": "2403.05733",
  "version": "v1",
  "published": "2024-03-09T00:07:24.000Z",
  "updated": "2024-03-09T00:07:24.000Z",
  "title": "Numerical cubature and hyperinterpolation over Spherical Polygons",
  "authors": [
    "Alvise Sommariva"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we report the results about numerical cubature over a spherical polygon $\\cal P$ approximating Australia and reconstruction of functions over such $\\cal P$, also affected by perturbations, via hyperinterpolation and some of its variants. The open-source Matlab software used in the numerical tests is available at the author's homepage.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-09T00:07:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spherical polygon",
      "numerical cubature",
      "hyperinterpolation",
      "low-cardinality positive cubature formula",
      "open-source matlab software"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}