{
  "id": "1904.10568",
  "version": "v1",
  "published": "2019-04-23T23:37:52.000Z",
  "updated": "2019-04-23T23:37:52.000Z",
  "title": "Zhang Neural Networks for Fast and Accurate Computations of the Field of Values",
  "authors": [
    "Frank Uhlig"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper a new and different neural network, called Zhang Neural Network (ZNN) is appropriated from discrete time-varying matrix problems and applied to the angle parameter-varying matrix field of values (FoV) problem. This problem acts as a test bed for newly discovered convergent 1-step ahead finite difference formulas of high truncation orders. The ZNN method that uses a look-ahead finite difference scheme of error order 6 gives us 15+ accurate digits of the FoV boundary in record time when applied to hermitean matrix flows $A(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-23T23:37:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "65F15",
      "65F30",
      "15A18"
    ],
    "keywords": [
      "zhang neural network",
      "accurate computations",
      "ahead finite difference formulas",
      "look-ahead finite difference scheme",
      "hermitean matrix flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}