{
  "id": "1512.04246",
  "version": "v1",
  "published": "2015-12-14T10:23:20.000Z",
  "updated": "2015-12-14T10:23:20.000Z",
  "title": "Numerical stability of iterative refinement with a relaxation for linear systems",
  "authors": [
    "Alicja Smoktunowicz",
    "Jakub Kierzkowski",
    "Iwona Wrobel"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson's iterative refinement. We assume that all computations are performed in fixed (working) precision arithmetic. Numerical tests were done in MATLAB to illustrate our theoretical results. A particular emphasis is given on convergence of iterative refinement with a relaxation. Our tests confirm that the choice omega=1 is the best choice from the point of numerical stability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-14T10:23:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F05",
      "65F10",
      "15A12"
    ],
    "keywords": [
      "numerical stability",
      "wilkinsons iterative refinement",
      "best choice",
      "extends existing results",
      "relaxation ir"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}