{
  "id": "2209.01616",
  "version": "v1",
  "published": "2022-06-10T13:54:43.000Z",
  "updated": "2022-06-10T13:54:43.000Z",
  "title": "Note on Error Bound for Trace Approximation of Products of Toeplitz Matrices",
  "authors": [
    "Tetsuya Takabatake"
  ],
  "categories": [
    "math.CA",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on $[-\\pi,\\pi]$ having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem~2 of \\cite{Lieberman-Phillips-2004}, its proof contains an inaccuracy as pointed out by \\cite{Ginovyan-Sahakyan-2013}. In the present paper, we reinvestigate the claim given in Theorem~2 of \\cite{Lieberman-Phillips-2004} and give an alternative proof of their claim.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-10T13:54:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toeplitz matrices",
      "trace approximation",
      "error bound",
      "integral limit approximations",
      "sharp error order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}