{"id":209999,"created":"2025-01-19T01:11:16.490337+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00209999","sets":["1164:2240:10556:10557"]},"path":["10557"],"owner":"44499","recid":"209999","title":["フィルタ対角化法に与える初期ベクトルの改良の模索"],"pubdate":{"attribute_name":"公開日","attribute_value":"2021-03-08"},"_buckets":{"deposit":"5862093b-13a8-451b-a602-857ad7e2baae"},"_deposit":{"id":"209999","pid":{"type":"depid","value":"209999","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"フィルタ対角化法に与える初期ベクトルの改良の模索","author_link":["530748"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"フィルタ対角化法に与える初期ベクトルの改良の模索"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"数値解析","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2021-03-08","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"東京都立大学数理科学専攻"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematical Sciences, Tokyo Metropolitan 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/209999/files/IPSJ-HPC21178001.pdf","label":"IPSJ-HPC21178001.pdf"},"date":[{"dateType":"Available","dateValue":"2023-03-08"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC21178001.pdf","filesize":[{"value":"1.5 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":"14"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"d83c1e0a-51f8-4052-aaf2-024801c93b57","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2021 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"村上, 弘"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10463942","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8841","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"フィルタ対角化法により一般固有値問題の固有対で指定区間に固有値があるものの近似を求める．その際にこれまでは，「必要な固有ベクトル」に関する事前知識を持たないと仮定して，フィルタに与えるべき「必要な固有ベクトル」すべてを含むベクトルの組として，成分が一様乱数であるベクトルの組の正規直交化により得られるものを用いてきた．しかし，その方法で生成されたベクトルの組が含む「必要な固有ベクトル」の割合は，行列次数の増加に伴い減少するので，そのことからフィルタを適用して得られたベクトルの組が含む「不要な固有ベクトル」の割合は増加する．それにより，精度の限られた数値計算では，フィルタ適用で得たベクトルの組を元にして構成される「必要な固有ベクトル」の張る不変部分空間の近似が悪くなり，近似固有対の精度も低下する．それ以外にも問題の規模が大きくなると，たとえばレゾルベントの作用を実現するための連立 1 次方程式の求解における丸め誤差の影響も増大する．（なお，直交化とフィルタを適用する組み合わせの処理を反復することで，近似不変部分空間とそれから得られる近似固有対の精度を段階的に向上できることは既に報告済みである [1][2]．）今回は，一様乱数を要素とするベクトルの組の正規直交化で得られたものに対して，さらに「必要な固有ベクトル」を含む割合を増すような処理を加える．ただしその処理の手間はあまり多くないものとする．そのような処理を加えて得られたベクトルの組に対してフィルタを適用する，という方法を模索する．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"17","bibliographic_titles":[{"bibliographic_title":"研究報告ハイパフォーマンスコンピューティング（HPC）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2021-03-08","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicVolumeNumber":"2021-HPC-178"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"updated":"2025-01-19T18:18:46.267169+00:00","links":{}}