{"created":"2025-01-19T01:14:02.970129+00:00","updated":"2025-01-19T17:15:54.653987+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00213138","sets":["1164:2240:10556:10713"]},"path":["10713"],"owner":"44499","recid":"213138","title":["Lagrange補間の係数計算のある簡単な数値的トリックについて"],"pubdate":{"attribute_name":"公開日","attribute_value":"2021-09-20"},"_buckets":{"deposit":"77538de4-040f-4ba1-8768-6e367bc866b0"},"_deposit":{"id":"213138","pid":{"type":"depid","value":"213138","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"Lagrange補間の係数計算のある簡単な数値的トリックについて","author_link":["544801"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Lagrange補間の係数計算のある簡単な数値的トリックについて"}]},"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":"2021-09-20","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/213138/files/IPSJ-HPC21181005.pdf","label":"IPSJ-HPC21181005.pdf"},"date":[{"dateType":"Available","dateValue":"2023-09-20"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC21181005.pdf","filesize":[{"value":"795.4 kB"}],"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":"3312f0bf-00c3-46dc-aacd-7490d42f23b2","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":"Lagrange 補間式の係数を求める際に，浮動小数点数の性質を用いた以下のような近似計算法が可能である．使用する補間の分点 xj，j=1, 2,..., n は互いに良く分離しているとする．そのとき関数 f(x) に対する Lagrange の補間多項式は p(x)=Σnj=1wj(l(x)/(x-xj))fj で与えられる．ここで l(x)≡Πnk=1(x-xk)，fj≡f(xj) である．そうして 1/wj=l'(xj) であるが，この値を分点 xj の値を極めて僅かにずらした点 yj での値 l'(yi) に置き換える．すると，l'(yj)～l(yj)/(yj-xj) である．この右辺の分母は分子に因子として含まれている．よって近似の仮定の下では，sj=l(yj)=Πnk=1(yj-xk) を求めて wj=(yj-xj)/sj とすれば良い．この方法の利点は，係数 wj を求める計算の中で，添字に依存する条件分岐やあるいは添字に依存したループ分割が回避できることである．そうして，補間多項式の x=z に於ける値 p(z)は，z がどの補間点にも一致や極端な近接がなければ，p(z)=l(z)Σnj=1wj/(z-xj)fj として計算できる．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"6","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":"2021-09-20","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"5","bibliographicVolumeNumber":"2021-HPC-181"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":213138,"links":{}}