{
  "id": "math-ph/9808008",
  "version": "v2",
  "published": "1998-08-20T07:59:12.000Z",
  "updated": "1998-08-21T15:50:05.000Z",
  "title": "A novel approach to estimate the stability of one-dimensional quantum inverse scattering",
  "authors": [
    "H. J. S. Dorren"
  ],
  "comment": "10 pages Latex, figures available upon request or on http://asterix.urc.tue.nl/~elechd/abstr13.html",
  "categories": [
    "math-ph",
    "math.MP",
    "math.NA"
  ],
  "abstract": "We present a novel method to estimate the stability of the Marchenko equation for finite data-sets. We show that we can derive a recursion relationship for the Fourier expansion coefficients of the kernel which is solved by the Marchenko equation. The method can easily be implemented numerically. Moreover, we discus the stability of the one-dimensional inverse scattering problem by using Lyapunov exponents. We give conditions on the scattering data to provide stable inversion results. A numerical example is given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-08-21T15:50:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional quantum inverse scattering",
      "novel approach",
      "marchenko equation",
      "fourier expansion coefficients",
      "one-dimensional inverse scattering problem"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.ph...8008D"
    }
  }
}