{
  "id": "2101.07949",
  "version": "v1",
  "published": "2021-01-20T03:29:29.000Z",
  "updated": "2021-01-20T03:29:29.000Z",
  "title": "Fast linear barycentric rational interpolation for singular functions via scaled transformations",
  "authors": [
    "Desong Kong",
    "Shuhuang Xiang"
  ],
  "comment": "24 pages, 32 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\\alpha$ for $\\alpha \\in (0,1)$ and $\\log(x)$. It just takes $O(N)$ flops and can achieve fast convergence rates with the choice the scaled parameter, where $N$ is the maximum degree of the denominator and numerator. The construction of the rational interpolant couples rational polynomials in the barycentric form of second kind with the transformed Jacobi-Gauss-Lobatto points. Numerical experiments are considered which illustrate the accuracy and efficiency of the algorithms. The convergence of the rational interpolation is also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-20T03:29:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32E30",
      "41A20",
      "41A50",
      "65N35",
      "65M70"
    ],
    "keywords": [
      "fast linear barycentric rational interpolation",
      "singular functions",
      "scaled transformations",
      "monotonic increasing scaled maps",
      "rational interpolant couples rational polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}