{"created":"2023-05-15T11:19:47.538731+00:00","id":235,"links":{},"metadata":{"_buckets":{"deposit":"ad8953dd-1cb7-4a55-8bee-7f010360f3fb"},"_deposit":{"created_by":2,"id":"235","owners":[2],"pid":{"revision_id":0,"type":"depid","value":"235"},"status":"published"},"_oai":{"id":"oai:nsu.repo.nii.ac.jp:00000235","sets":["6:7:78"]},"author_link":["395","396"],"control_number":"235","item_2_biblio_info_4":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2014-02","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"43","bibliographicPageEnd":"107","bibliographicPageStart":"87","bibliographic_titles":[{"bibliographic_title":"新潟産業大学経済学部紀要"}]}]},"item_2_description_10":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"論文(Article)","subitem_description_type":"Other"}]},"item_2_description_3":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"1673年村瀬義益（佐渡→江戸→下総（現在の千葉県））は『算法勿憚改』[8]を著した．この書で村瀬は，3次方程式から2種類の2乗の漸化式と3次方程式の変形を導いた．この変形式の文章は短文にもかかわらず長年未解読であつた．しかし2009年5月に藤井康生が解読に成功した[5]．村瀬は変形式でホーナー法も研究している．江戸時代初期にこのような研究がされているのである．鈴木武雄[9]は「村瀬は和算史上だけでなく，世界数学史上でも稀有な存在である」と評価している．日本にはこのような独創性のある和算家がいるのである．変形式の解読により研究が進展した．2009年中頃に3つの式より，我々は村瀬の2乗の漸化式が，ニュートン・ラフソン法(1690)の拡張に繋がることを発見し，q乗の土倉・堀口法として与えた[3]．さらに本稿では§1においてニュートン・ラフソン法の改良であるHalley法の拡張を与える．§2は拡張Halley法の収束式および収束比較式(等式の場合)を与える．§3は収束比較式(等式の場合)の数値計算を行う．和算から現代数学（西洋数学）の論文を書くことは極めて難しく，本稿を含めたこれまでの一連の研究が最初であろう．さらに一連の研究は江戸時代の日本の文化が高いことも示している．もし数学教室の図書館を自由に利用可能なら，ここで現代数学の良質な論文を読む方が多くの収穫を得られる．","subitem_description_type":"Abstract"}]},"item_2_description_7":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_full_name_2":{"attribute_name":"著者別名","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"396","nameIdentifierScheme":"WEKO"}],"names":[{"name":"HORIGUCHI, Shunji"}]}]},"item_2_publisher_9":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"新潟産業大学附属東アジア経済文化研究所"}]},"item_2_source_id_6":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10492758","subitem_source_identifier_type":"NCID"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"堀口, 俊二","creatorNameLang":"ja"}],"nameIdentifiers":[{"nameIdentifier":"395","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2019-10-24"}],"displaytype":"detail","filename":"43_87-107.pdf","filesize":[{"value":"2.7 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"43_87-107.pdf","url":"https://nsu.repo.nii.ac.jp/record/235/files/43_87-107.pdf"},"version_id":"7ed33b5d-96b1-4ad6-8c46-3c1fbdcabf9e"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Halley法と拡張Halley法(土倉1･堀口･村瀬･Halley法) の収束比較式Ⅰ(等式の場合)とその数値計算","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Halley法と拡張Halley法(土倉1･堀口･村瀬･Halley法) の収束比較式Ⅰ(等式の場合)とその数値計算","subitem_title_language":"ja"},{"subitem_title":"The formulasⅠ(in the case of an equation) to compare the convergence of Halley method and the extended Halley method(Tsuchikura-Horiguchi- Murase -Halley method) and the numerical calculations","subitem_title_language":"en"}]},"item_type_id":"2","owner":"2","path":["78"],"pubdate":{"attribute_name":"公開日","attribute_value":"2014-04-07"},"publish_date":"2014-04-07","publish_status":"0","recid":"235","relation_version_is_last":true,"title":["Halley法と拡張Halley法(土倉1･堀口･村瀬･Halley法) の収束比較式Ⅰ(等式の場合)とその数値計算"],"weko_creator_id":"2","weko_shared_id":-1},"updated":"2023-07-20T05:08:29.285064+00:00"}