{
  "id": "2003.07913",
  "version": "v1",
  "published": "2020-03-17T19:48:00.000Z",
  "updated": "2020-03-17T19:48:00.000Z",
  "title": "Regularization of linear and nonlinear ill-posed problems by mollification",
  "authors": [
    "Walter Cedric Simo Tao Lee"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.FA",
    "math.OC"
  ],
  "abstract": "In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed equation $T(f) =g$ where $T$ can be nonlinear. The regularized solutions we define extend the work of Bonnefond and Mar\\'echal \\cite{xapi}, and trace their origins in the variational formulation of mollification, which to the best of our knowledge, was first introduced by Lannes et al. \\cite{lannes}. In addition to consistency results, for the first time, we provide some convergence rates for a mollification method defined through a variational formulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-17T19:48:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A29",
      "47A52",
      "65F22",
      "65N20"
    ],
    "keywords": [
      "nonlinear ill-posed problems",
      "review existing mollification regularization methods",
      "variational formulation",
      "quickly review existing mollification regularization",
      "general ill-posed equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}