{
  "id": "1206.1762",
  "version": "v2",
  "published": "2012-06-08T14:05:03.000Z",
  "updated": "2012-06-19T15:00:39.000Z",
  "title": "On the condition number and perturbation of matrix functions for Hermitian matrices",
  "authors": [
    "Elias Jarlebring",
    "Emanuel H. Rubensson"
  ],
  "comment": "Shortly after submission of this manuscript we discovered that Lemma 2 does not hold under the stated conditions. In order to have the time to carefully work out and understand the reason for this error and hopefully correct it, we have decided to withdraw the manuscript",
  "categories": [
    "math.NA"
  ],
  "abstract": "Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation ||f(A+E)-f(A)|| expressed in terms of eigenvalues of A and A+E. The results are general and under certain conditions hold for an arbitrary unitarily invariant matrix norm ||\\cdot||. We illustrate the use of the formulas with an application to the error analysis of calculations in electronic structure theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-19T15:00:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F60"
    ],
    "keywords": [
      "matrix function",
      "hermitian matrices",
      "perturbation",
      "arbitrary unitarily invariant matrix norm",
      "absolute structured condition number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1762J"
    }
  }
}