Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations

Takeshi Ogita, Shinichi Oishi, Yasunori Ushiro

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.

    Original languageEnglish
    Pages (from-to)229-239
    Number of pages11
    JournalReliable Computing
    Volume9
    Issue number3
    DOIs
    Publication statusPublished - 2003 Jun

    Fingerprint

    System of Linear Equations
    Linear equations
    Error Bounds
    Approximate Solution
    Rounding
    Sharp Bound
    Positive definite
    Fast Algorithm
    Numerical Results
    Coefficient

    ASJC Scopus subject areas

    • Software
    • Safety, Risk, Reliability and Quality

    Cite this

    Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations. / Ogita, Takeshi; Oishi, Shinichi; Ushiro, Yasunori.

    In: Reliable Computing, Vol. 9, No. 3, 06.2003, p. 229-239.

    Research output: Contribution to journalArticle

    @article{4558f84a26c2422f8661afdbf9c0db18,
    title = "Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations",
    abstract = "This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.",
    author = "Takeshi Ogita and Shinichi Oishi and Yasunori Ushiro",
    year = "2003",
    month = "6",
    doi = "10.1023/A:1024655416554",
    language = "English",
    volume = "9",
    pages = "229--239",
    journal = "Reliable Computing",
    issn = "1385-3139",
    publisher = "Springer Netherlands",
    number = "3",

    }

    TY - JOUR

    T1 - Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations

    AU - Ogita, Takeshi

    AU - Oishi, Shinichi

    AU - Ushiro, Yasunori

    PY - 2003/6

    Y1 - 2003/6

    N2 - This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.

    AB - This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.

    UR - http://www.scopus.com/inward/record.url?scp=0038174786&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0038174786&partnerID=8YFLogxK

    U2 - 10.1023/A:1024655416554

    DO - 10.1023/A:1024655416554

    M3 - Article

    AN - SCOPUS:0038174786

    VL - 9

    SP - 229

    EP - 239

    JO - Reliable Computing

    JF - Reliable Computing

    SN - 1385-3139

    IS - 3

    ER -