{"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00219081","sets":["934:1119:10960:10961"]},"path":["10961"],"owner":"44499","recid":"219081","title":["実対称固有値分解に対する反復改良法の高速化"],"pubdate":{"attribute_name":"公開日","attribute_value":"2022-07-28"},"_buckets":{"deposit":"26a27a85-ea1b-47a0-bc41-5f933aeb76dc"},"_deposit":{"id":"219081","pid":{"type":"depid","value":"219081","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"実対称固有値分解に対する反復改良法の高速化","author_link":["571084","571088","571085","571087","571086","571083"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"実対称固有値分解に対する反復改良法の高速化"},{"subitem_title":"Acceleration of Iterative Refinement for Symmetric Eigenvalue Decomposition","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"反復改良法，高精度計算，実対称固有値分解","subitem_subject_scheme":"Other"}]},"item_type_id":"3","publish_date":"2022-07-28","item_3_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"芝浦工業大学大学院理工学研究科"},{"subitem_text_value":"芝浦工業大学数理科学科"},{"subitem_text_value":"東京女子大学数理科学科"}]},"item_3_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Engineering and Science, Shibaura Institute of Technology","subitem_text_language":"en"},{"subitem_text_value":"Department of Mathematical Sciences, Shibaura Institute of Technology","subitem_text_language":"en"},{"subitem_text_value":"Division of Mathematical Sciences, Tokyo Woman's Christian University","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/219081/files/IPSJ-TACS1501002.pdf","label":"IPSJ-TACS1501002.pdf"},"date":[{"dateType":"Available","dateValue":"2024-07-28"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-TACS1501002.pdf","filesize":[{"value":"2.3 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"660","billingrole":"5"},{"tax":["include_tax"],"price":"330","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"16"},{"tax":["include_tax"],"price":"0","billingrole":"11"},{"tax":["include_tax"],"price":"0","billingrole":"14"},{"tax":["include_tax"],"price":"0","billingrole":"15"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"b405329a-1e41-46d4-930a-f671a05ac260","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2022 by the Information Processing Society of Japan"}]},"item_3_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"内野, 佑基"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"尾崎, 克久"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"荻田, 武史"}],"nameIdentifiers":[{}]}]},"item_3_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yuki, Uchino","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Katsuhisa, Ozaki","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Takeshi, Ogita","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_3_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11833852","subitem_source_identifier_type":"NCID"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_6501","resourcetype":"journal article"}]},"item_3_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1882-7829","subitem_source_identifier_type":"ISSN"}]},"item_3_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"本論文では，荻田と相島が提案した実対称固有値分解に対する反復改良法の高速化手法を提案する．標準固有値問題に対する数値計算法は現在までに様々なものが提案されている．近年，荻田と相島はある程度正確な近似固有対に対して2次収束性を持つ反復改良法を提案した．この手法は1反復あたり主に4回の高精度行列積で構成されている．本研究では，固有値に重複・クラスタが存在しない問題について，荻田・相島法と同程度の収束性をより高速に得る反復改良法を設計した．本手法は1反復あたり主に3回の高精度行列積で構成されている．また，エラーフリー行列積を用いた反復改良法の要求精度の調査と実装の工夫によりさらなる高速化を図った．数値実験では2反復した際のそれらの有効性を示す．最後に，一般化固有値問題への拡張も紹介する．","subitem_description_type":"Other"}]},"item_3_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"We propose algorithms to accelerate iterative refinement for symmetric eigenvalue decomposition proposed by Ogita and Aishima. Various numerical algorithms have been developed for standard eigenvalue problems. Recently, Ogita and Aishima proposed an efficient refinement algorithm which converges quadratically if a modestly accurate initial guess is given. That is constructed via four highly accurate matrix multiplications per an iteration. In this study, we design the variant of that refinement algorithm for matrices whose all eigenvalues are simple. That is constructed via three highly accurate matrix multiplications per an iteration. The proposed method achieves results of almost the same quality as the original algorithm proposed by Ogita and Aishima if eigenvalues are all simple and not clustered. Moreover, we investigate the required arithmetic precision for refinement algorithms using error-free matrix multiplications and further accelerate those by devising implementations. Numerical experiments illustrate the efficiency of the proposed algorithm for two iterations. We also extend our idea to generalized eigenvalue problems.","subitem_description_type":"Other"}]},"item_3_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"12","bibliographic_titles":[{"bibliographic_title":"情報処理学会論文誌コンピューティングシステム（ACS）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2022-07-28","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicVolumeNumber":"15"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":219081,"updated":"2025-01-19T14:55:56.813950+00:00","links":{},"created":"2025-01-19T01:19:24.961126+00:00"}