{
  "id": "0801.3088",
  "version": "v3",
  "published": "2008-01-20T15:05:48.000Z",
  "updated": "2008-08-03T14:30:37.000Z",
  "title": "On Steepest-Descent-Kaczmarz Methods for Regularizing Systems of Nonlinear Ill-posed Equations",
  "authors": [
    "A. De Cezaro",
    "M. Haltmeier",
    "A. Leitao",
    "O. Scherzer"
  ],
  "comment": "22 pages (8 figures). For this version we have corrected some typos and also have corrected Equation (25) in the proof of Theorem 3.3",
  "journal": "Applied Mathematics and Computation 202 (2008), pp. 596-607",
  "categories": [
    "math.NA"
  ],
  "abstract": "We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a linear problem related to photoacoustic tomography and a non-linear problem related to the testing of semiconductor devices.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-08-03T14:30:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J20",
      "47J06"
    ],
    "keywords": [
      "nonlinear ill-posed equations",
      "steepest-descent-kaczmarz methods",
      "regularizing systems",
      "convergent regularization method",
      "operator equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3088D"
    }
  }
}