{"updated":"2025-01-22T23:54:24.379695+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00016353","sets":["581:927:929"]},"path":["929"],"owner":"1","recid":"16353","title":["Durand - Kerner法とAberth法を用いた超高次方程式の数値計算"],"pubdate":{"attribute_name":"公開日","attribute_value":"1979-09-15"},"_buckets":{"deposit":"90047aff-6b75-42bb-8fcf-4ac781c1cc8d"},"_deposit":{"id":"16353","pid":{"type":"depid","value":"16353","revision_id":0},"owners":[1],"status":"published","created_by":1},"item_title":"Durand - Kerner法とAberth法を用いた超高次方程式の数値計算","author_link":["0","0"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Durand - Kerner法とAberth法を用いた超高次方程式の数値計算"},{"subitem_title":"On Numerical Computation of a High Degree Polynomial Equation by the Methods of Durand - Kerner and Aberth","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"論文","subitem_subject_scheme":"Other"}]},"item_type_id":"2","publish_date":"1979-09-15","item_2_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"東京都立農芸高等学校"}]},"item_2_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Tokyo Metropolitan Nogei Agricultural Upper Secondary School","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"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/16353/files/IPSJ-JNL2005004.pdf"},"date":[{"dateType":"Available","dateValue":"1981-09-15"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-JNL2005004.pdf","filesize":[{"value":"451.2 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":"8"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"540bd663-83dc-490b-afbb-1afef3386d14","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 1979 by the Information Processing Society of Japan"}]},"item_2_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"小野, 令美"}],"nameIdentifiers":[{}]}]},"item_2_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Ono, Harumi","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_2_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN00116647","subitem_source_identifier_type":"NCID"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_6501","resourcetype":"journal article"}]},"item_2_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1882-7764","subitem_source_identifier_type":"ISSN"}]},"item_2_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"高次方程式の数値解法で最近注目されてきたものに全根同時反復型解法Durand-Kerner法とAberth法がある(DKA法と略す).例としてChebyshevの数値積分公式の分点を与える高次方程式をとりあげ 1000次以上におよぶ超高次方程式をこの解法で解いた.さらに低次のものについてはsystem に備えられているsubroutine libraryとも比較してみた.その結果次数が高くなるにつれ従来の解法では得られた解の精度が正しく評価できなかったが DKA法ではGerschgorin circle半径の範囲内で正しく求められた.超高次方程式についてはDKA法でも桁落ちのため必要な桁数の解が得られなくなるので 一部多倍長演算が必要になる.このようにして最高1024次のものまでについてGezschgorin circIe半径が完全に分離した解を得た.その結果解はn→∞極限で根が並ぶと予想されている曲線に近づくことが数値的に確かめられた.これらの結果を述べる.さらにこの数値実験を通して得られたこの種の大規模計算を行う際に注意すべきことがらを述べる.このう3.1問題の特殊性の利用3.2多倍長演算の効果的使用(計算の各段階での必要な計算桁数の解析)3.3計算法の手間の検討などが特に重要な知見である.","subitem_description_type":"Other"}]},"item_2_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"404","bibliographic_titles":[{"bibliographic_title":"情報処理学会論文誌"}],"bibliographicPageStart":"399","bibliographicIssueDates":{"bibliographicIssueDate":"1979-09-15","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"5","bibliographicVolumeNumber":"20"}]},"relation_version_is_last":true,"weko_creator_id":"1"},"created":"2025-01-18T22:49:38.946429+00:00","id":16353,"links":{}}