2023-06-05T12:48:43Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:000948262020-10-27T05:02:56Z00934:00989:07128:07246
On Implementation and Evaluation of Inverse Iteration Algorithm with Compact WY OrthogonalizationOn Implementation and Evaluation of Inverse Iteration Algorithm with Compact WY Orthogonalizationeng[オリジナル論文] parallel processing, inverse iteration, reorthogonalization, compact WY representation, Householder transformationhttp://id.nii.ac.jp/1001/00094807/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=94826&item_no=1&attribute_id=1&file_no=1Copyright (c) 2013 by the Information Processing Society of JapanGraduate School of Informatics, Kyoto UniversityGraduate School of Informatics, Kyoto UniversityGraduate School of Informatics, Kyoto UniversityHiroyuki, IshigamiKinji, KimuraYoshimasa, NakamuraIn this paper, we introduce an inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel processors. To overcome the sequential bottleneck created by modified Gram-Schmidt orthogonalization in classical inverse iteration, we propose the use of the compact WY representation in the reorthogonalization process, based on the Householder transformation. This change results in drastically reduced synchronization cost during parallel processing.In this paper, we introduce an inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel processors. To overcome the sequential bottleneck created by modified Gram-Schmidt orthogonalization in classical inverse iteration, we propose the use of the compact WY representation in the reorthogonalization process, based on the Householder transformation. This change results in drastically reduced synchronization cost during parallel processing.AA11464803情報処理学会論文誌数理モデル化と応用（TOM）6225352013-08-211882-77802013-08-15