{
  "id": "ACAInv",
  "url": "https://www.bmtdynamics.org/cgi-bin/display.pl?name=ACAInv",
  "title": "Verification of Invertibility of Complicated Functions over Large Domains",
  "pdfs": [
    {
      "url": "https://www.bmtdynamics.org/pub/papers/ACAInv/ACAInv.pdf",
      "filename": "ACAInv.pdf",
      "size_bytes": null
    }
  ],
  "page_text": "Publications\nReprint Server\nVerification of Invertibility of Complicated Functions over Large Domains\nAbstract\nA new method to decide the invertibility of a given high-dimensional\nfunction over a domain is presented. The problem arises in the field\nof verified solution of differential algebraic equations (DAEs)\nrelated to the need to perform projections of certain constraint\nmanifolds over large domains. The question of invertibility is\nreduced to a verified linear algebra problem involving first\npartials of the function under consideration. Different from\nconventional approaches, the elements of the resulting matrices are\nTaylor models for the derivatives of the functions.\nThe linear algebra problem is solved based on Taylor model methods,\nand it will be shown the method is able to decide invertibility with\na conciseness that often goes substantially beyond what can be\nobtained with other interval methods. The theory of the approach is\npresented. Comparisons with three other interval-based methods are\nperformed for practical examples, illustrating the applicability of\nthe new method.\nJ. Hoefkens, M. Berz,\nReliable Computing\n8\n(1) (2002) 1-16\nDownload\nClick on the icon to download the corresponding file.\nDownload Adobe PDF version (246763 Bytes).\nGo Back\nto the reprint server.\nGo Back\nto the home page.\nThis page is maintained by\nKyoko Makino\n. Please contact her if there are any problems with it."
}