Fast algorithms for floating-point interval matrix multiplication

Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shinichi Oishi

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We discuss several methods for real interval matrix multiplication. First, earlier studies of fast algorithms for interval matrix multiplication are introduced: naive interval arithmetic, interval arithmetic by midpointradius form by OishiRump and its fast variant by OgitaOishi. Next, three new and fast algorithms are developed. The proposed algorithms require one, two or three matrix products, respectively. The point is that our algorithms quickly predict which terms become dominant radii in interval computations. We propose a hybrid method to predict which algorithm is suitable for optimizing performance and width of the result. Numerical examples are presented to show the efficiency of the proposed algorithms.

    Original languageEnglish
    Pages (from-to)1795-1814
    Number of pages20
    JournalJournal of Computational and Applied Mathematics
    Volume236
    Issue number7
    DOIs
    Publication statusPublished - 2012 Jan

    Fingerprint

    Interval Matrix
    Matrix multiplication
    Floating point
    Fast Algorithm
    Interval Arithmetic
    Interval Computation
    Predict
    Matrix Product
    Hybrid Method
    Radius
    Numerical Examples
    Term

    Keywords

    • Interval arithmetic
    • INTLAB
    • Matrix multiplication
    • Verified numerical computations

    ASJC Scopus subject areas

    • Computational Mathematics
    • Applied Mathematics

    Cite this

    Fast algorithms for floating-point interval matrix multiplication. / Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shinichi.

    In: Journal of Computational and Applied Mathematics, Vol. 236, No. 7, 01.2012, p. 1795-1814.

    Research output: Contribution to journalArticle

    Ozaki, Katsuhisa ; Ogita, Takeshi ; Rump, Siegfried M. ; Oishi, Shinichi. / Fast algorithms for floating-point interval matrix multiplication. In: Journal of Computational and Applied Mathematics. 2012 ; Vol. 236, No. 7. pp. 1795-1814.
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