{
  "id": "2011.05870",
  "version": "v1",
  "published": "2020-11-11T16:05:59.000Z",
  "updated": "2020-11-11T16:05:59.000Z",
  "title": "On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations",
  "authors": [
    "A. Leitao",
    "B. F. Svaiter"
  ],
  "comment": "22 pages, 3 figures",
  "journal": "Inverse Problems 32 (2016), no. 1, 025004",
  "doi": "10.1088/0266-5611/32/2/025004",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone condition. We show that the proposed iteration is a convergent regularization method. Numerical tests are presented for a non-linear inverse problem related to the Dirichlet-to-Neumann map, indicating a superior performance of the proposed method when compared with other well established iterations. Our preliminary investigation indicates that the resulting iteration is a promising alternative for computing stable solutions of large scale systems of nonlinear ill-posed equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T16:05:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J20",
      "47J06"
    ],
    "keywords": [
      "nonlinear ill-posed equations",
      "projective landweber-kaczmarz methods",
      "solving systems",
      "large scale systems",
      "non-linear inverse problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}