IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v30y1988i6p481-491.html
   My bibliography  Save this article

Review on stochastic approach to round-off error analysis and its applications

Author

Listed:
  • Vignes, J.

Abstract

Because of round-off error propagation in floating-point arithmetic, any result provided by a computer always contains an error. The Permutation-Perturbation method, also known under the CESTAC (Contrôle et Estimation Stochastique des Arrondis de Calcul) method is a precious tool: (i) for evaluating the accuracy of results provided by direct algorithms performed by a computer, (ii) for breaking off correctly any iterative process, and for evaluating the accuracy of the results, and (iii) for determining the optimal step or the optimal mesh in the approximate algorithms. A review of this method and of these applications is presented in this paper.

Suggested Citation

  • Vignes, J., 1988. "Review on stochastic approach to round-off error analysis and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 481-491.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:6:p:481-491
    DOI: 10.1016/0378-4754(88)90070-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475488900705
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(88)90070-5?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.

    References listed on IDEAS

    as
    1. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    2. Vergnes, J. & Dumontet, J., 1979. "Finding an optimal partition for a numerical integration using the trapezoidal rule," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 231-241.
    3. Tolla, Pierre, 1983. "Linear and non-linear programming software validity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 39-42.
    4. Ton-That, Long, 1988. "Numerical accuracy control in fixed-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 553-561.
    5. Bois, P. & Vignes, J., 1980. "A software for evaluating local accuracy in the fourier transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(2), pages 141-150.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alt, R. & Lamotte, J.-L., 2001. "Experiments on the evaluation of functional ranges using a random interval arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(1), pages 17-34.
    2. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
    2. Vergnes, J., 1980. "Determination d'un pas optimum d'integration pour la methode de Simpson," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(3), pages 177-188.
    3. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    4. Alliot, Nicole, 1988. "Data error analysis in unconstrained optimization problems with the CESTAC method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 531-539.

    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:30:y:1988:i:6:p:481-491. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.