{
  "id": "1502.07838",
  "version": "v1",
  "published": "2015-02-27T09:29:07.000Z",
  "updated": "2015-02-27T09:29:07.000Z",
  "title": "Rectangular maximum-volume submatrices and their applications",
  "authors": [
    "A. Yu. Mikhalev",
    "I. V. Oseledets"
  ],
  "comment": "11 pages, 1 figure, submitted to SIAM J. Matrix Analysis",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A definition of $p$-volume of rectangular matrices is given. We generalize the results for square maximum-volume submatrices to the case rectangular maximal-volume submatrices and provide estimates for the growth of the coefficients. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online at \\url{https://bitbucket.org/muxas/rect_maxvol}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-27T09:29:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F99",
      "45A05"
    ],
    "keywords": [
      "rectangular maximum-volume submatrices",
      "applications",
      "case rectangular maximal-volume submatrices",
      "square maximum-volume submatrices",
      "rectangular matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}