{
  "id": "1209.3995",
  "version": "v1",
  "published": "2012-09-18T15:42:46.000Z",
  "updated": "2012-09-18T15:42:46.000Z",
  "title": "A Randomized Parallel Algorithm with Run Time $O(n^2)$ for Solving an $n \\times n$ System of Linear Equations",
  "authors": [
    "Joerg Fliege"
  ],
  "categories": [
    "math.NA",
    "cs.DS"
  ],
  "abstract": "In this note, following suggestions by Tao, we extend the randomized algorithm for linear equations over prime fields by Raghavendra to a randomized algorithm for linear equations over the reals. We also show that the algorithm can be parallelized to solve a system of linear equations $A x = b$ with a regular $n \\times n$ matrix $A$ in time $O(n^2)$, with probability one. Note that we do not assume that $A$ is symmetric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-18T15:42:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear equations",
      "randomized parallel algorithm",
      "run time",
      "randomized algorithm",
      "prime fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3995F"
    }
  }
}