{"created":"2025-01-19T01:46:26.232583+00:00","updated":"2025-01-19T07:34:48.145378+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00241686","sets":["1164:1579:11464:11813"]},"path":["11813"],"owner":"44499","recid":"241686","title":["Taylor展開法による数値計算"],"pubdate":{"attribute_name":"公開日","attribute_value":"2024-12-09"},"_buckets":{"deposit":"c4957acc-3d41-42ea-a337-40277131814f"},"_deposit":{"id":"241686","pid":{"type":"depid","value":"241686","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"Taylor展開法による数値計算","author_link":["665800"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Taylor展開法による数値計算"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"高精度計算","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2024-12-09","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"神奈川工科大学創造工学部自動車システム開発工学科"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Department of Vehicle System Engineering, Faculty of Creative Engneering, Kanagawa Institute of Technology","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/241686/files/IPSJ-ARC24259021.pdf","label":"IPSJ-ARC24259021.pdf"},"date":[{"dateType":"Available","dateValue":"2026-12-09"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-ARC24259021.pdf","filesize":[{"value":"958.7 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":"16"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"0c756e95-7c7f-436a-95db-3cac541f01f4","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2024 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"平山, 弘"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10096105","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":"2188-8574","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"Taylor 展開式を使った数値解析は，常微分方程式の数値計算で昔からよく使われたように思える．これらの研究からいろいろな関数などを Taylor 展開する方法は簡単で容易にできるようになった．この方法は常微分方程式の分野でも主流の計算方法にはなってはいないが精計算精度，計算時間的にも非常に優れている方法である．微分代数方程式も容易に高精度で計算出来る．微分係数が容易に計算出来ると，微分を含む公式を利用できるようになる．オイラー・マクローリンの総和公式はそのような公式である．この公式を使って数値積分を計算することが出来る．逆に使えば級数の和を計算することも出来る．これまでの数値計算で微分係数を使う Newton 法は，1 次の Taylor 級数を使って 1 次方程式で近似する方法である．Taylor 展開式をパデ展開式に変換することによって，高次の解法が得られる．逆関数を Taylor 展開することによって，高精度の Newton 法が得られる．逆関数をパデ展開することによって，安定性の良い Newton法が得られる．Taylor 級数法は数値計算に高精度な微分係数を高速に計算する方法で多くの分野で利用可能だと思われる．いろいろな分野で利用されることを期待する．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"7","bibliographic_titles":[{"bibliographic_title":"研究報告システム・アーキテクチャ（ARC）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2024-12-09","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"21","bibliographicVolumeNumber":"2024-ARC-259"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"id":241686,"links":{}}