A method of obtaining verified solutions for linear systems suited for Java

K. Ozaki, T. Ogita, S. Miyajima, Shinichi Oishi, S. M. Rump

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.

    Original languageEnglish
    Pages (from-to)337-344
    Number of pages8
    JournalJournal of Computational and Applied Mathematics
    Volume199
    Issue number2
    DOIs
    Publication statusPublished - 2007 Feb 15

    Fingerprint

    Java
    Linear systems
    Linear Systems
    Rounding
    Switches
    Java programming language
    Programming Languages
    Switch
    Approximate Solution
    Computer programming languages
    Numerical methods
    Approximate Inverse
    Gaussian elimination
    Numerical Computation
    Optimization Techniques
    Error Bounds
    Computational Cost
    Numerical Methods
    Numerical Experiment
    Costs

    Keywords

    • Java
    • Linear system
    • Verified computation

    ASJC Scopus subject areas

    • Applied Mathematics
    • Computational Mathematics
    • Numerical Analysis

    Cite this

    A method of obtaining verified solutions for linear systems suited for Java. / Ozaki, K.; Ogita, T.; Miyajima, S.; Oishi, Shinichi; Rump, S. M.

    In: Journal of Computational and Applied Mathematics, Vol. 199, No. 2, 15.02.2007, p. 337-344.

    Research output: Contribution to journalArticle

    Ozaki, K. ; Ogita, T. ; Miyajima, S. ; Oishi, Shinichi ; Rump, S. M. / A method of obtaining verified solutions for linear systems suited for Java. In: Journal of Computational and Applied Mathematics. 2007 ; Vol. 199, No. 2. pp. 337-344.
    @article{08fcb0b9a71249f386dc133092850b04,
    title = "A method of obtaining verified solutions for linear systems suited for Java",
    abstract = "Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.",
    keywords = "Java, Linear system, Verified computation",
    author = "K. Ozaki and T. Ogita and S. Miyajima and Shinichi Oishi and Rump, {S. M.}",
    year = "2007",
    month = "2",
    day = "15",
    doi = "10.1016/j.cam.2005.08.034",
    language = "English",
    volume = "199",
    pages = "337--344",
    journal = "Journal of Computational and Applied Mathematics",
    issn = "0377-0427",
    publisher = "Elsevier",
    number = "2",

    }

    TY - JOUR

    T1 - A method of obtaining verified solutions for linear systems suited for Java

    AU - Ozaki, K.

    AU - Ogita, T.

    AU - Miyajima, S.

    AU - Oishi, Shinichi

    AU - Rump, S. M.

    PY - 2007/2/15

    Y1 - 2007/2/15

    N2 - Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.

    AB - Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.

    KW - Java

    KW - Linear system

    KW - Verified computation

    UR - http://www.scopus.com/inward/record.url?scp=33749679665&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33749679665&partnerID=8YFLogxK

    U2 - 10.1016/j.cam.2005.08.034

    DO - 10.1016/j.cam.2005.08.034

    M3 - Article

    VL - 199

    SP - 337

    EP - 344

    JO - Journal of Computational and Applied Mathematics

    JF - Journal of Computational and Applied Mathematics

    SN - 0377-0427

    IS - 2

    ER -