{
  "id": "1209.2480",
  "version": "v1",
  "published": "2012-09-12T02:17:54.000Z",
  "updated": "2012-09-12T02:17:54.000Z",
  "title": "Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)",
  "authors": [
    "Jing Li"
  ],
  "comment": "17 pages. arXiv admin note: substantial text overlap with arXiv:1208.3672, arXiv:1208.3518",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 0<p<1. In the case p>1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is evaluated. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-12T02:17:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65H05",
      "65F10",
      "65F30"
    ],
    "keywords": [
      "unique positive definite solution",
      "perturbation analysis",
      "nonlinear matrix equation",
      "sharper perturbation bound",
      "explicit expressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2480L"
    }
  }
}