Tight and efficient enclosure of matrix multiplication by using optimized BLAS

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms.

    Original languageEnglish
    Pages (from-to)237-248
    Number of pages12
    JournalNumerical Linear Algebra with Applications
    Volume18
    Issue number2
    DOIs
    Publication statusPublished - 2011 Mar

    Fingerprint

    Matrix multiplication
    Enclosure
    Enclosures
    Digital arithmetic
    Interval Matrix
    Floating-point Arithmetic
    Floating point
    Exact Results
    Upper and Lower Bounds
    Numerical Examples
    Costs

    Keywords

    • Interval arithmetic
    • Matrix multiplication
    • Verified numerical computation

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Applied Mathematics

    Cite this

    Tight and efficient enclosure of matrix multiplication by using optimized BLAS. / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shinichi.

    In: Numerical Linear Algebra with Applications, Vol. 18, No. 2, 03.2011, p. 237-248.

    Research output: Contribution to journalArticle

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