著者

Tomonori Kouya

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.8, pp.21-24, 2016 (Released:2016-05-13)

参考文献数

9

被引用文献数

5

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It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplications. We have already shown that they are also very effective for software-based multiple precision floating-point arithmetic environments such as the MPFR/GMP library. In this paper, we show that we can obtain the same effectiveness for double-double (DD) and quadruple-double (QD) environments supported by the QD library, and that parallelization can increase the speed of these multiple precision matrix multiplications. Finally, we demonstrate that our implemented parallelized Strassen and Winograd algorithms can increase the speed of parallelized LU decomposition.

著者

Tomonori Kouya

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.6, pp.81-84, 2014 (Released:2014-12-17)

参考文献数

6

被引用文献数

2 5

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The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as double-precision matrix multiplication by using these algorithms, no research to date has been undertaken to accelerate multiple precision matrix multiplication. In this paper, we propose a multiple precision matrix multiplication program for matrices of any size and test its performance. We also reveal special properties of our program through its application to LU decomposition.

著者

幸谷 智紀 Tomonori KOUYA

出版者

静岡理工科大学

雑誌

静岡理工科大学紀要 = The Bulletin of the Shizuoka Institute of Science and Technology (ISSN:24351539)

巻号頁・発行日

vol.28, pp.23-31, 2020-05-25