{
  "id": "1511.07694",
  "version": "v1",
  "published": "2015-11-24T13:20:47.000Z",
  "updated": "2015-11-24T13:20:47.000Z",
  "title": "Geometrical inverse preconditioning for symmetric positive definite matrices",
  "authors": [
    "Jean-Paul Chehab",
    "Marcos Raydan"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We focus on inverse preconditioners based on minimizing $F(X) = 1-\\cos(XA,I)$, where $XA$ is the preconditioned matrix and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$ on a suitable compact set. For that we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of $F(X)$ on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-24T13:20:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F08",
      "65F50",
      "15A09"
    ],
    "keywords": [
      "symmetric positive definite matrices",
      "geometrical inverse preconditioning",
      "analyze gradient-type methods",
      "suitable compact set",
      "inverse preconditioners"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}