{
  "id": "2011.12573",
  "version": "v1",
  "published": "2020-11-25T08:34:53.000Z",
  "updated": "2020-11-25T08:34:53.000Z",
  "title": "On a fast and nearly division-free algorithm for the characteristic polynomial",
  "authors": [
    "Fredrik Johansson"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We review the Preparata-Sarwate algorithm, a simple $O(n^{3.5})$ method for computing the characteristic polynomial, determinant and adjugate of an $n \\times n$ matrix using only ring operations together with exact divisions by small integers. The algorithm is a baby-step giant-step version of the more well-known Faddeev-Leverrier algorithm. We make a few comments about the algorithm and evaluate its performance empirically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-25T08:34:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic polynomial",
      "division-free algorithm",
      "well-known faddeev-leverrier algorithm",
      "baby-step giant-step version",
      "preparata-sarwate algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}