{
  "id": "1107.5363",
  "version": "v1",
  "published": "2011-07-27T01:30:10.000Z",
  "updated": "2011-07-27T01:30:10.000Z",
  "title": "Convergence of the Iterative Rational Krylov Algorithm",
  "authors": [
    "Garret Flagg",
    "Christopher Beattie",
    "Serkan Gugercin"
  ],
  "journal": "Systems and Control Letters, Volume: 61, Issue: 6, pp. 688-691, 2012",
  "doi": "10.1016/j.sysconle.2012.03.005",
  "categories": [
    "math.NA"
  ],
  "abstract": "The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory model reduction approach to the optimal $\\mathcal{H}_2$ approximation problem. Even though the method has been illustrated to show rapid convergence in various examples, a proof of convergence has not been provided yet. In this note, we show that in the case of state-space symmetric systems, IRKA is a locally convergent fixed point iteration to a local minimum of the underlying $\\mathcal{H}_2$ approximation problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-27T01:30:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iterative rational krylov algorithm",
      "convergence",
      "interpolatory model reduction approach",
      "approximation problem",
      "locally convergent fixed point iteration"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5363F"
    }
  }
}