{
  "id": "1812.08645",
  "version": "v1",
  "published": "2018-12-20T15:47:25.000Z",
  "updated": "2018-12-20T15:47:25.000Z",
  "title": "On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes",
  "authors": [
    "Stefan Kunis",
    "Dominik Nagel"
  ],
  "comment": "18 pages, 7 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are \"off the grid\", pairs of nodes nearly collide, and the studied condition number grows linearly with the inverse separation distance. We provide reasonable sharp constants that are independent from the number of nodes as long as non-colliding nodes are well-separated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-20T15:47:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "65T40",
      "42A15"
    ],
    "keywords": [
      "nearly-colliding nodes",
      "inverse separation distance",
      "condition number grows",
      "complex unit circle",
      "rectangular vandermonde matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}