metadata/CTMSPB09.json

{
  "id": "CTMSPB09",
  "url": "https://www.bmtdynamics.org/cgi-bin/display.pl?name=CTMSPB09",
  "title": "Taylor Models and Computaions in the Complex Plane",
  "pdfs": [
    {
      "url": "https://www.bmtdynamics.org/pub/papers/CTMSPB09/CTMSPB09.pdf",
      "filename": "CTMSPB09.pdf",
      "size_bytes": null
    }
  ],
  "page_text": "Publications\nReprint Server\nTaylor Models and Computaions in the Complex Plane\nAbstract\nIn this note we show how Taylor model methods can successfully alleviate\r\nthe problems of conventional interval arithmetic in the complex plane being susceptible to\r\nsignificant overestimations caused by the dependency problems in the elementary operations.\r\nThe use of Taylor models on the other hand results in self-validated methods that fully utilize\r\nthe rich structure of the complex numbers.\nTo show how high order methods can be used for self-validated computations in the\r\ncomplex plane, we extend real-valued Taylor model methods to complex ones. The extension\r\nprovides the tools to compute enclosures of the results of elementary operations and standard\r\nfunctions. We show how the new methods provide sharp and validated descriptions of image\r\nsets of analytic functions even after extended computations.\nA. Ovsyannikov, M. Berz,\nBulletin of St. Petersburg University\n,\n10,4\n(2009) 172-185\nDownload\nClick on the icon to download the corresponding file.\nDownload Adobe PDF version (392634 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."
}