IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v30y1988i6p553-561.html
   My bibliography  Save this article

Numerical accuracy control in fixed-point arithmetic

Author

Listed:
  • Ton-That, Long

Abstract

The purpose of this paper is to look at the problem of propagation of round-off errors in fixed-point arithmetic and at various problems of checking solutions of equations already treated by La Porte and Vignes in the case of floating-point arithmetic. We first consider the probabilistic model for the numerical fixed-point representation on a computer, the evaluation of the mean value and of the standard deviation for the absolute error of the assignment operator A, and of elementary operators of arithmetic. We then compute the statistical estimate of the error in the computation of an inner product, and this leads us to the problem of checking the accuracy of the solution of linear systems and of algebraic equations.

Suggested Citation

  • Ton-That, Long, 1988. "Numerical accuracy control in fixed-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 553-561.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:6:p:553-561
    DOI: 10.1016/0378-4754(88)90076-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475488900766
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(88)90076-6?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, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
    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. 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.

    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. Pichat, M., 1988. "All possible computed results in correct floating-point summation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 541-552.
    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. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
    4. Toutounian, Faezeh, 1988. "Practical methods for evaluating the accuracy of the eigenelements of a symmetric matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 493-504.
    5. 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.
    6. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    7. Alt, René, 1988. "Floating-point error propagation in iterative methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 505-517.
    8. 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.
    9. Salkuyeh, Davod Khojasteh & Toutounian, Faezeh & Yazdi, Hamed Shariat, 2008. "A procedure with stepsize control for solving n one-dimensional IVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(2), pages 167-176.
    10. Abadie, J. & Dekhli, F., 1988. "A variant of the CESTAC method and its application to constrained optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 519-529.
    11. Albertsen, Niels Christian & Chesneaux, Jean-Marie & Christiansen, Søren & Wirgin, Armand, 1999. "Comparison of four software packages applied to a scattering problem1Professor Ralph E. Kleinman, University of Delaware, USA, in memoriam.1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 307-317.
    12. 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.
    13. 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:553-561. 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.