{
  "id": "2011.09893",
  "version": "v1",
  "published": "2020-11-19T15:26:53.000Z",
  "updated": "2020-11-19T15:26:53.000Z",
  "title": "Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis",
  "authors": [
    "M. Haltmeier",
    "A. Leitao",
    "O. Scherzer"
  ],
  "comment": "11 pages, 1 figure",
  "journal": "Inverse Problems and Imaging 1 (2007), no. 2, 289-298",
  "doi": "10.3934/ipi.2007.1.289",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and incorporating a loping strategy. The first technique is a Kaczmarz-type method, equipped with a novel stopping criteria. The second method is obtained using an embedding strategy, and again a Kaczmarz-type approach. We prove well-posedness, stability and convergence of both methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-19T15:26:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J20",
      "47J06"
    ],
    "keywords": [
      "nonlinear ill-posed equations",
      "convergence analysis",
      "analyze novel iterative regularization techniques",
      "nonlinear ill-posed operator equations",
      "basic idea consists"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}