{
  "id": "1208.3672",
  "version": "v1",
  "published": "2012-08-17T01:50:48.000Z",
  "updated": "2012-08-17T01:50:48.000Z",
  "title": "Solutions and perturbation analysis of the matrix equation X - \\sum_{i=1}^m A_i^* X^{-1} A_i = Q",
  "authors": [
    "Jing Li"
  ],
  "comment": "23 pages. arXiv admin note: text overlap with arXiv:1208.3518",
  "categories": [
    "math.NA"
  ],
  "abstract": "Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q. This paper shows that there exists a unique positive definite solution to the equation without any restriction on A_{i}. Three perturbation bounds for the unique solution to the equation are evaluated. A backward error of an approximate solution for the unique solution to the equation is derived. Explicit expressions of the condition number for the unique solution to the equation are obtained. The theoretical results are illustrated by numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-17T01:50:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A24",
      "47H14",
      "65H05"
    ],
    "keywords": [
      "perturbation analysis",
      "unique solution",
      "unique positive definite solution",
      "nonlinear matrix equation",
      "perturbation bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3672L"
    }
  }
}