{
  "id": "1407.0671",
  "version": "v1",
  "published": "2014-07-02T18:28:35.000Z",
  "updated": "2014-07-02T18:28:35.000Z",
  "title": "Optimal rates of convergence of matrices with applications",
  "authors": [
    "Heinz H. Bauschke",
    "J. Y. Bello Cruz",
    "Tran T. A. Nghia",
    "Hung M. Phan",
    "Xianfu Wang"
  ],
  "comment": "32 pages, 3 figures",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of semi-simpleness of all eigenvalues having the second-largest modulus after 1. We also provide applications of our general results to analyze the optimal convergence rates for several relaxed alternating projection methods and the generalized Douglas-Rachford splitting methods for finding the projection on the intersection of two subspaces. Numerical experiments confirm our convergence analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-02T18:28:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F10",
      "65F15"
    ],
    "keywords": [
      "optimal rates",
      "optimal convergence rate",
      "applications",
      "linear convergence rates",
      "convergence analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0671B"
    }
  }
}