{
  "id": "2308.07287",
  "version": "v1",
  "published": "2023-08-14T17:19:52.000Z",
  "updated": "2023-08-14T17:19:52.000Z",
  "title": "On a semidefinite programming characterizations of the numerical radius and its dual norm",
  "authors": [
    "Shmuel Friedland",
    "Chi-Kwong Li"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.OC"
  ],
  "abstract": "We give a semidefinite programming characterization of the dual norm of numerical radius for matrices. This characterization yields a new proof of semidefinite characterization of the numerical radius for matrices, which follows from Ando's characterization. We show that the computation of the numerical radius and its dual norm within $\\varepsilon$ precision are polynomially time computable in the data and $|\\log \\varepsilon |$ using the short step, primal interior point method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-14T17:19:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "15A69",
      "68Q25",
      "68W25",
      "90C22",
      "90C51"
    ],
    "keywords": [
      "semidefinite programming characterization",
      "numerical radius",
      "dual norm",
      "primal interior point method",
      "andos characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}