{"links":{},"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00222645","sets":["1164:2240:10902:11046"]},"path":["11046"],"owner":"44499","recid":"222645","title":["固有値問題のフィルタを用いた固有対の近似の構成について"],"pubdate":{"attribute_name":"公開日","attribute_value":"2022-11-24"},"_buckets":{"deposit":"194f820c-cf5c-47bc-860a-2d2ac5123fef"},"_deposit":{"id":"222645","pid":{"type":"depid","value":"222645","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"固有値問題のフィルタを用いた固有対の近似の構成について","author_link":["584381"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"固有値問題のフィルタを用いた固有対の近似の構成について"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"数値計算","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2022-11-24","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/222645/files/IPSJ-HPC22187002.pdf","label":"IPSJ-HPC22187002.pdf"},"date":[{"dateType":"Available","dateValue":"2024-11-24"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC22187002.pdf","filesize":[{"value":"1.9 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":"3af09872-db78-421f-a00e-9ec51ddf70e9","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2022 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":"行列の固有値問題において，固有ベクトルの伝達率がその固有値だけに依存して決まる線形作用素をうまく構成して，それを固有値が指定された区間にある固有ベクトルを抽出するためのフィルタとして用いる．必要な固有対についての知識を仮定しないで，ランダムなベクトルを十分多く生成してそれらを正規直交化した組を作ってそれにフィルタを作用させると，得られるベクトルの組は不要な固有ベクトルの含有率が低くて必要な固有ベクトルの含有率の高いものになる．そのようなベクトルの組からうまく線形結合を選んで必要な固有ベクトルで張られる不変部分空間の近似基底で条件の良いものを構成し，それに Rayleigh-Ritz 法を適用すると必要な固有対の近似が得られることになる．しかしフィルタの特性が悪くて，不要な固有ベクトルの含有率を十分に小さくできない場合や，必要な固有ベクトル相互に対する伝達率の大きさが著しく異なる場合には，ランダムなベクトルの組を正規直交化してそれにフィルタを適用して得られるベクトルの組が張る空間は不変部分空間の良い精度の近似にならず，その結果として得られる近似固有対も精度が悪くなる．そのような場合には，ベクトルの組に正規直交化を施してからフィルタを適用するという 2 つの操作を組み合わせとして反復することで精度を改良する方法があり，それは非常に効果的である．その各反復において用いるフィルタは同じでなくてもよいので，それについての考察も行う．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"22","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":"2022-11-24","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicVolumeNumber":"2022-HPC-187"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"created":"2025-01-19T01:22:35.105820+00:00","updated":"2025-01-19T13:40:03.485787+00:00","id":222645}