{
  "id": "2009.08089",
  "version": "v1",
  "published": "2020-09-17T06:20:15.000Z",
  "updated": "2020-09-17T06:20:15.000Z",
  "title": "Quantile-based Iterative Methods for Corrupted Systems of Linear Equations",
  "authors": [
    "Jamie Haddock",
    "Deanna Needell",
    "Elizaveta Rebrova",
    "William Swartworth"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving such large-scale systems of linear equations $\\mathbf{A}\\mathbf{x}=\\mathbf{b}$ that are inconsistent due to corruptions in the measurement vector $\\mathbf{b}$. We develop several variants of iterative methods that converge to the solution of the uncorrupted system of equations, even in the presence of large corruptions. These methods make use of a quantile of the absolute values of the residual vector in determining the iterate update. We present both theoretical and empirical results that demonstrate the promise of these iterative approaches.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-17T06:20:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F10",
      "68W20",
      "60B20"
    ],
    "keywords": [
      "linear equations",
      "quantile-based iterative methods",
      "corrupted systems",
      "large-scale linear systems",
      "data science"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}