IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v35y1993i5p435-450.html
   My bibliography  Save this article

Numerics with automatic result verification

Author

Listed:
  • Kulisch, Ulrich
  • Rall, L.B.

Abstract

Floating-point arithmetic is the fast way to perform scientific and engineering calculations. Today, individual floating-point operations are maximally accurate as a rule. However, after only two or just a few operations, the result can be completely wrong. Computers now carry out up to 1011 floating-point operations in a second. Thus, particular attention must be paid to the reliability of the computed results. In recent years, techniques have been developed in numerical analysis which make it possible for the computer itself to verify the correctness of computed results for numerous problems and applications. Moreover, the computer frequently establishes the existence and uniqueness of the solution in this way. For example, a verified solution of a system of ordinary differential equations is just as valid as a solution obtained by a computer algebra system, which as a rule still requires a valid formula evaluation. Furthermore, the numerical routine remains applicable even if the problem does not have a closed-form solution.

Suggested Citation

  • Kulisch, Ulrich & Rall, L.B., 1993. "Numerics with automatic result verification," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 435-450.
    • Handle: RePEc:eee:matcom:v:35:y:1993:i:5:p:435-450
    DOI: 10.1016/0378-4754(93)90042-S
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037847549390042S
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(93)90042-S?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    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:eee:matcom:v:35:y:1993:i:5:p:435-450. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.