{
  "id": "math/0508099",
  "version": "v1",
  "published": "2005-08-04T20:06:08.000Z",
  "updated": "2005-08-04T20:06:08.000Z",
  "title": "Reconstruction of tridiagonal matrices from spectral data",
  "authors": [
    "Ricardo S. Leite",
    "Nicolau C. Saldanha",
    "Carlos Tomei"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.NA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Jacobi matrices are parametrized by their eigenvalues and norming constants (first coordinates of normalized eigenvectors): this coordinate system breaks down at reducible tridiagonal matrices. The set of real symmetric tridiagonal matrices with prescribed simple spectrum is a compact manifold, admitting an open covering by open dense sets ${\\cal U}^\\pi_\\Lambda$ centered at diagonal matrices $\\Lambda^\\pi$, where $\\pi$ spans the permutations. {\\it Bidiagonal coordinates} are a variant of norming constants which parametrize each open set ${\\cal U}^\\pi_\\Lambda$ by the Euclidean space. The reconstruction of a Jacobi matrix from inverse data is usually performed by an algorithm introduced by de Boor and Golub. In this paper we present a reconstruction procedure from bidiagonal coordinates and show how to employ it as an alternative to the de Boor-Golub algorithm. The inverse bidiagonal algorithm rates well in terms of speed and accuracy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-04T20:06:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F18",
      "15A29"
    ],
    "keywords": [
      "spectral data",
      "reconstruction",
      "inverse bidiagonal algorithm rates",
      "bidiagonal coordinates",
      "real symmetric tridiagonal matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8099L"
    }
  }
}