Numerical Investigation into the Mixed Precision GMRES(m) Method Using FP64 and FP32

• Item type: Trans(1)
• 公開日: 2022-07-28
• タイトル: Numerical Investigation into the Mixed Precision GMRES(m) Method Using FP64 and FP32
• タイトル / 言語: en
• タイトル: Numerical Investigation into the Mixed Precision GMRES(m) Method Using FP64 and FP32
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: sparse linear solver, iterative refinement, low precision computing, mixed precision algorithm
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: Graduate School of Information Science and Technology, Hokkaido University
• 著者所属: Information Initiative Center, Hokkaido University／JST Presto
• 著者所属: School of Mathematical Sciences, Ocean University of China
• 著者所属: Information Initiative Center, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Science and Technology, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Information Initiative Center, Hokkaido University / JST Presto
• 著者所属(英): en
• 著者所属(英): School of Mathematical Sciences, Ocean University of China
• 著者所属(英): en
• 著者所属(英): Information Initiative Center, Hokkaido University
• 著者名: Yingqi, Zhao; Takeshi, Fukaya; Linjie, Zhang; Takeshi, Iwashita
• 著者名(英): Yingqi, Zhao; Takeshi, Fukaya; Linjie, Zhang; Takeshi, Iwashita
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: In this paper, a mixed precision variant of the GMRES(m) method using FP64 and FP32 is investigated. Through numerical experiments for various test matrices and different settings of the restart frequency m, its numerical behavior is examined in detail and compared with that of the conventional GMRES(m) method using only FP64. From the obtained numerical results, it is confirmed that if a problem is solved by the conventional GMRES(m) method, basically the mixed precision GMRES(m) can also solve it. In addition, in the case of using small m, the number of the total iterations is almost equivalent between the two methods. However, when m grows, a different tendency is observed; the number of the iterations decreases in the conventional methods but increases in the mixed precision method. These results and observations provide new insights of the mixed precision GMRES(m) method, which will be helpful for the efficient use in applications and the further improvement of the method.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.30(2022) (online); ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: In this paper, a mixed precision variant of the GMRES(m) method using FP64 and FP32 is investigated. Through numerical experiments for various test matrices and different settings of the restart frequency m, its numerical behavior is examined in detail and compared with that of the conventional GMRES(m) method using only FP64. From the obtained numerical results, it is confirmed that if a problem is solved by the conventional GMRES(m) method, basically the mixed precision GMRES(m) can also solve it. In addition, in the case of using small m, the number of the total iterations is almost equivalent between the two methods. However, when m grows, a different tendency is observed; the number of the iterations decreases in the conventional methods but increases in the mixed precision method. These results and observations provide new insights of the mixed precision GMRES(m) method, which will be helpful for the efficient use in applications and the further improvement of the method.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.30(2022) (online); ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA11833852
• 書誌情報: 情報処理学会論文誌コンピューティングシステム（ACS）; 巻 15, 号 1, 発行日 2022-07-28
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7829
• 出版者 / 言語: ja
• 出版者: 情報処理学会