IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-57201-2_12.html
   My bibliography  Save this book chapter

Complexity of Derivatives Generated by Symbolic Differentiation

In: Computer Algebra in Scientific Computing

Author

Listed:
  • Herbert Fischer

    (Technische Universität München, Fakultüt für Mathematik)

  • Hubert Warsitz

    (Technische Universität München, Fakultüt für Mathematik)

Abstract

The computational solution of many mathematical problems involves derivatives. Programs for computing derivatives may be (1) hand-Coded, (2) set up via function calls and divided differences, or (3) obtained using symbolic differentiation. In practice, the divided differences approach is still the standard technique. But in many cases, derivatives can be computed cheaper and more accurately by symbolic differentiation. In this paper we investigate the complexity of algorithms for computing derivatives of rational functions. In particular, we deal with the forward mode and the reverse mode of symbolic differentiation. We discuss bounds on the amount of work within the described algorithms in terms of rational operations.

Suggested Citation

  • Herbert Fischer & Hubert Warsitz, 2000. "Complexity of Derivatives Generated by Symbolic Differentiation," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing, pages 129-144, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57201-2_12
    DOI: 10.1007/978-3-642-57201-2_12
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-57201-2_12. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.