Subspace Correction Preconditioning for Solving a Sequence of Asymmetric Linear Systems Using the Bi-CGSTAB Method

• Item type: Trans(1)
• 公開日: 2023-11-29
• タイトル: Subspace Correction Preconditioning for Solving a Sequence of Asymmetric Linear Systems Using the Bi-CGSTAB Method
• タイトル / 言語: en
• タイトル: Subspace Correction Preconditioning for Solving a Sequence of Asymmetric Linear Systems Using the Bi-CGSTAB Method
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: Bi-CGSTAB method, Subspace correction preconditioning, Vector sampling, A sequence of asymmetric linear systems
• 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
• 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
• 著者所属(英): en
• 著者所属(英): Information Initiative Center, Hokkaido University
• 著者名: Hirotoshi, Tamori; Takeshi, Fukaya; Takeshi, Iwashita
• 著者名(英): Hirotoshi, Tamori; Takeshi, Fukaya; Takeshi, Iwashita
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: This paper focuses on a solution process of a sequence of linear systems having an asymmetric coefficient matrix. We propose a new subspace correction (SC) preconditioning method based on error vector sampling for asymmetric coefficient matrices. In the method, we identify approximate left and right singular vectors associated with small singular values using the sampled error vectors calculated after the first solution step. Using these singular vectors, we construct auxiliary matrices to specify the subspace used in the SC preconditioning. We applied the proposed preconditioning method to an ILU(0)-Bi-CGSTAB solver in additive Schwarz manner. To examine the proposed preconditioning method, we conducted numerical tests using matrices downloaded from the SuiteSparse Matrix Collection database. Numerical tests showed that the proposed method could reduce the number of iterations to convergence and the solution time in many test cases, which confirms the effectiveness of the method. Moreover, the proposed method succeeded to get convergence for some test problems that the ILU(0) preconditioned solver could not solve.; ------------------------------; 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.31(2023) (online); ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: This paper focuses on a solution process of a sequence of linear systems having an asymmetric coefficient matrix. We propose a new subspace correction (SC) preconditioning method based on error vector sampling for asymmetric coefficient matrices. In the method, we identify approximate left and right singular vectors associated with small singular values using the sampled error vectors calculated after the first solution step. Using these singular vectors, we construct auxiliary matrices to specify the subspace used in the SC preconditioning. We applied the proposed preconditioning method to an ILU(0)-Bi-CGSTAB solver in additive Schwarz manner. To examine the proposed preconditioning method, we conducted numerical tests using matrices downloaded from the SuiteSparse Matrix Collection database. Numerical tests showed that the proposed method could reduce the number of iterations to convergence and the solution time in many test cases, which confirms the effectiveness of the method. Moreover, the proposed method succeeded to get convergence for some test problems that the ILU(0) preconditioned solver could not solve.; ------------------------------; 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.31(2023) (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 16, 号 2, 発行日 2023-11-29
• 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