{
  "id": "1108.3570",
  "version": "v2",
  "published": "2011-08-17T20:28:25.000Z",
  "updated": "2012-01-18T18:16:16.000Z",
  "title": "Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction",
  "authors": [
    "Maarten V. de Hoop",
    "Lingyun Qiu",
    "Otmar Scherzer"
  ],
  "categories": [
    "math.FA",
    "math.NA"
  ],
  "abstract": "We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under which these strongly converge, locally, to the solutions within an appropriate distance. We express the conditions for convergence in terms of H\\\"{o}lder stability of the inverse maps, which ties naturally to the analysis of inverse problems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-18T18:16:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problems",
      "hölder stability",
      "local analysis",
      "iterative reconstruction",
      "model functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012InvPr..28d5001D"
    }
  }
}