Matrix multiplication with guaranteed accuracy by level 3 BLAS

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    This paper is concerned with an accurate computing for matrix multiplication. We show that matrix multiplication can be transformed into a summation of floating-point matrices by mainly using level 3 operations in BLAS. We call it 'errorfree transformation of matrix multiplication'. By combining this error-free transformation and accurate summation algorithms for floating-point numbers, we can obtain an accurate result of matrix multiplication. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

    Original languageEnglish
    Title of host publicationAIP Conference Proceedings
    Pages1128-1133
    Number of pages6
    Volume1504
    DOIs
    Publication statusPublished - 2012
    EventInternational Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009 - Rhodes
    Duration: 2009 Sep 292009 Oct 4

    Other

    OtherInternational Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009
    CityRhodes
    Period09/9/2909/10/4

    Fingerprint

    multiplication
    matrices
    floating

    Keywords

    • Accurate Algorithms
    • Matrix Computations

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Ozaki, K., Ogita, T., & Oishi, S. (2012). Matrix multiplication with guaranteed accuracy by level 3 BLAS. In AIP Conference Proceedings (Vol. 1504, pp. 1128-1133) https://doi.org/10.1063/1.4772125

    Matrix multiplication with guaranteed accuracy by level 3 BLAS. / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shinichi.

    AIP Conference Proceedings. Vol. 1504 2012. p. 1128-1133.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ozaki, K, Ogita, T & Oishi, S 2012, Matrix multiplication with guaranteed accuracy by level 3 BLAS. in AIP Conference Proceedings. vol. 1504, pp. 1128-1133, International Conference of Computational Methods in Sciences and Engineering 2009, ICCMSE 2009, Rhodes, 09/9/29. https://doi.org/10.1063/1.4772125
    Ozaki K, Ogita T, Oishi S. Matrix multiplication with guaranteed accuracy by level 3 BLAS. In AIP Conference Proceedings. Vol. 1504. 2012. p. 1128-1133 https://doi.org/10.1063/1.4772125
    Ozaki, Katsuhisa ; Ogita, Takeshi ; Oishi, Shinichi. / Matrix multiplication with guaranteed accuracy by level 3 BLAS. AIP Conference Proceedings. Vol. 1504 2012. pp. 1128-1133
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