{
  "id": "2001.04184",
  "version": "v1",
  "published": "2020-01-13T12:32:30.000Z",
  "updated": "2020-01-13T12:32:30.000Z",
  "title": "Rational spectral filters with optimal convergence rate",
  "authors": [
    "Konrad Kollnig",
    "Paolo Bientinesi",
    "Edoardo Di Napoli"
  ],
  "comment": "23 pages, 7 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through non-linear least square optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence ratio and eliminate the parametric dependence on weight functions. Further, we provide an efficient way to deal with the box-constraints which play a central role for the use of iterative linear solvers in contour-based eigensolvers. Indeed, these parameter-free filters consistently minimize the number of iterations and the number of FLOPs to reach convergence in the eigensolver. As a byproduct, our rational filters allow for a simple solution to load balancing when the solution of an interior eigenproblem is approached by the slicing of the sought after spectral interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-13T12:32:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F15",
      "41A20",
      "65Y05"
    ],
    "keywords": [
      "optimal convergence rate",
      "rational spectral filters",
      "rational filters",
      "sparse eigenvalue problems",
      "worst-case convergence ratio"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}