2016年5月
Performance evaluation of multiple precision matrix multiplications using parallelized Strassen and Winograd algorithms
JSIAM Letters
- 巻
- 8
- 号
- 開始ページ
- 21
- 終了ページ
- 24
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.14495/jsiaml.8.21
It is well known that Strassen and Winograd algorithms can reduce the computational<br />
costs associated with dense matrix multiplication. We have already shown<br />
that they are also very effective for software-based multiple precision floating-point<br />
arithmetic environments such as the MPFR/GMP library. In this paper, we show<br />
that we can obtain the same effectiveness for double-double (DD) and quadrupledouble<br />
(QD) environments supported by the QD library, and that parallelization<br />
can increase the speed of these multiple precision matrix multiplications. Finally, we<br />
demonstrate that our implemented parallelized Strassen and Winograd algorithms<br />
can increase the speed of parallelized LU decomposition.
costs associated with dense matrix multiplication. We have already shown<br />
that they are also very effective for software-based multiple precision floating-point<br />
arithmetic environments such as the MPFR/GMP library. In this paper, we show<br />
that we can obtain the same effectiveness for double-double (DD) and quadrupledouble<br />
(QD) environments supported by the QD library, and that parallelization<br />
can increase the speed of these multiple precision matrix multiplications. Finally, we<br />
demonstrate that our implemented parallelized Strassen and Winograd algorithms<br />
can increase the speed of parallelized LU decomposition.
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