Fast verified solutions of linear systems

Takeshi Ogita, Shinichi Oishi

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

    Original languageEnglish
    Pages (from-to)169-190
    Number of pages22
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume26
    Issue number2-3
    Publication statusPublished - 2009 Oct

    Fingerprint

    Linear systems
    Sparse Linear Systems
    Linear Systems
    Numerical Computation
    Numerical Solution
    Digital arithmetic
    Floating-point Arithmetic
    Error Bounds
    Fast Algorithm
    Numerical Results
    Standards

    Keywords

    • Self-validating methods
    • Verified numerical computation
    • Verified solutions of linear systems

    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

    Cite this

    Fast verified solutions of linear systems. / Ogita, Takeshi; Oishi, Shinichi.

    In: Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3, 10.2009, p. 169-190.

    Research output: Contribution to journalArticle

    @article{5a5ff983aaf54d158ae44e8dc9954894,
    title = "Fast verified solutions of linear systems",
    abstract = "This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.",
    keywords = "Self-validating methods, Verified numerical computation, Verified solutions of linear systems",
    author = "Takeshi Ogita and Shinichi Oishi",
    year = "2009",
    month = "10",
    language = "English",
    volume = "26",
    pages = "169--190",
    journal = "Japan Journal of Industrial and Applied Mathematics",
    issn = "0916-7005",
    publisher = "Springer Japan",
    number = "2-3",

    }

    TY - JOUR

    T1 - Fast verified solutions of linear systems

    AU - Ogita, Takeshi

    AU - Oishi, Shinichi

    PY - 2009/10

    Y1 - 2009/10

    N2 - This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

    AB - This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

    KW - Self-validating methods

    KW - Verified numerical computation

    KW - Verified solutions of linear systems

    UR - http://www.scopus.com/inward/record.url?scp=77149148747&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77149148747&partnerID=8YFLogxK

    M3 - Article

    VL - 26

    SP - 169

    EP - 190

    JO - Japan Journal of Industrial and Applied Mathematics

    JF - Japan Journal of Industrial and Applied Mathematics

    SN - 0916-7005

    IS - 2-3

    ER -