{"links":{},"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00231116","sets":["1164:2240:11176:11408"]},"path":["11408"],"owner":"44499","recid":"231116","title":["T-S行列に対する列選択付きハウスホルダ型QR分解法の並列処理に向けた実装法について"],"pubdate":{"attribute_name":"公開日","attribute_value":"2023-11-28"},"_buckets":{"deposit":"af6e98dc-42d4-4971-bd0d-ecfeab8b6ac7"},"_deposit":{"id":"231116","pid":{"type":"depid","value":"231116","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"T-S行列に対する列選択付きハウスホルダ型QR分解法の並列処理に向けた実装法について","author_link":["623429"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"T-S行列に対する列選択付きハウスホルダ型QR分解法の並列処理に向けた実装法について"},{"subitem_title":"Some implementation of QR factorization methods for a tall-skinny matrix by using Householder transformations with column selections for parallel processing","subitem_title_language":"en"}]},"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":"2023-11-28","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/231116/files/IPSJ-HPC23192038.pdf","label":"IPSJ-HPC23192038.pdf"},"date":[{"dateType":"Available","dateValue":"2025-11-28"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC23192038.pdf","filesize":[{"value":"1.3 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":"14"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"eb5d9934-df51-4a10-b045-e6a9f5fc3842","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2023 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 QR 分解を鏡映変換を繰り返し用いて行うハウスホルダ QR 法は，分解の精度と正規直交基底の精度が両方とも非常に良いことが知られている．通常のハウスホルダ QR 法では与えられた行列の列の順に従って鏡映変換を作成してそれ以降の列に適用する操作の繰り返すことで上三角化した行列 R を作り，その後で鏡映変換を逆順に用いて得られる正規直交な列が並んだ Q を作ることで行列分解 A = QR が得られる．これに対して毎回の鏡映変換を決めるための列として 2 乗ノルムが最も大きいものを選びだす操作を追加した方法があり，それにより P を列の選択で用いた互換を蓄積した列の置換とするとき，分解 AP=QR が得られる．この列の選択を行って得られる上三角行列 R はその構成法から，対角要素が単調減少（非増加）であり，列内で大きさが最大の要素が対角要素であるという良い性質を持つ．列の選択の操作を追加した分だけ計算の手間は増えるが，性質の良い R を利用する計算は精度の面では有利になるので，A の列の線型独立性が良くない場合に対して特に使われる．列の選択を行わない QR 分解を行う場合に，行列 A が極めて縦長であれば TSQR 法と呼ばれる計算手法が良く知られている．それはまず A を縦方向にブロック分割して，各ブロックで独立に QR 分解を行って得られた上三角行列を集めて縦に並べた行列を作り，それに対して再度 QR 分解を行う，のような階層的な手法であり，計算の主要部を複数の処理装置に分配して行う並行処理が容易にできる．そこで本報告では，列の選択を行う QR 分解を行う場合についても同様に，行列 A が極めて縦長であれば，TSQR 法と同様の階層的な計算手法が可能であることを示す．ただし今回は階層が 2 つの場合についてだけ扱う．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"21","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":"2023-11-28","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"38","bibliographicVolumeNumber":"2023-HPC-192"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"created":"2025-01-19T01:31:17.181986+00:00","updated":"2025-01-19T10:52:20.619478+00:00","id":231116}