{
  "id": "0903.1244",
  "version": "v1",
  "published": "2009-03-06T16:24:55.000Z",
  "updated": "2009-03-06T16:24:55.000Z",
  "title": "Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials",
  "authors": [
    "Houssam Khalil",
    "Bernard Mourrain",
    "Michelle Schatzman"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we re-investigate the resolution of Toeplitz systems $T u =g$, from a new point of view, by correlating the solution of such problems with syzygies of polynomials or moving lines. We show an explicit connection between the generators of a Toeplitz matrix and the generators of the corresponding module of syzygies. We show that this module is generated by two elements of degree $n$ and the solution of $T u=g$ can be reinterpreted as the remainder of an explicit vector depending on $g$, by these two generators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-06T16:24:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toeplitz-block-toeplitz matrices",
      "polynomials",
      "correlation",
      "generators",
      "toeplitz systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1244K"
    }
  }
}