Interval arithmetic is a fundamental and reliable mathematical machinery for scientific computing and for addressing uncertainty in general. In order to apply interval mathematics to real life uncertainty problems, one needs a computerized (machine) version thereof, and so, this article is devoted to some mathematical notions concerning the algebraic system of machine interval arithmetic. After formalizing some purely mathematical ingredients of particular importance for the purpose at hand, we give formal characterizations of the algebras of real intervals and machine intervals along with describing the need for interval computations to cope with uncertainty problems. Thereupon, we prove some algebraic and order-theoretic results concerning the structure of machine intervals.


    Access

    Download


    Export, share and cite



    Title :

    On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic


    Contributors:
    Hend Dawood (author)

    Publication date :

    2019-04-01


    Remarks:

    oai:zenodo.org:2656089
    Online Mathematics Journal 01(02) 1–13



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    629




    Determination of Inspection Order by Interval Arithmetic Neural Networks

    Ishibuchi, H. / Miyazaki, A. | British Library Online Contents | 1995


    The interval arithmetic package

    Yohe, J. M. | TIBKAT | 1977



    Recent Topic on Circuit Analysis Application of Interval Arithmetic

    Okumura, K. | British Library Online Contents | 1996