{
  "id": "1208.3518",
  "version": "v1",
  "published": "2012-08-17T01:38:11.000Z",
  "updated": "2012-08-17T01:38:11.000Z",
  "title": "Perturbation analysis of the matrix equation X - \\sum_{i=1}^m A_i^* X^{p_i} A_i = Q",
  "authors": [
    "Jing Li"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{p_{i}}A_{i}=Q with p_{i}>0. Sufficient and necessary conditions for the existence of positive definite solutions to the equation with p_{i}>0 are derived. Two perturbation bounds for the unique solution to the equation with 0<p_{i}<1 are evaluated. The backward error of an approximate solution for the unique solution to the equation with 0<p_{i}<1 is given. Explicit expressions of the condition number for the equation with 0<p_{i}<1 are obtained. The theoretical results are illustrated by numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-17T01:38:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A24",
      "47H14",
      "65H05"
    ],
    "keywords": [
      "perturbation analysis",
      "unique solution",
      "nonlinear matrix equation",
      "perturbation bounds",
      "condition number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3518L"
    }
  }
}