{
  "id": "2202.13161",
  "version": "v1",
  "published": "2022-02-26T15:27:24.000Z",
  "updated": "2022-02-26T15:27:24.000Z",
  "title": "Higher order Hermite-Fejer Interpolation on the unit circle",
  "authors": [
    "Swarnima Bahadur",
    "Varun"
  ],
  "comment": "11 pages, 1 figure, submitted to springer journal CONSTRUCTIVE APPROXIMATION",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit circle with boundary points at $ \\pm1 $. Values of the polynomial and its first four derivatives are fixed by the interpolation conditions at the nodes. Convergence of the process is obtained for analytic functions on a suitable domain, and the rate of convergence is estimated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-26T15:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A05",
      "97N50",
      "41A10",
      "30E10"
    ],
    "keywords": [
      "unit circle",
      "higher order hermite-fejer interpolation process",
      "boundary points",
      "analytic functions",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}