{"created":"2025-01-18T23:22:24.754693+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00059690","sets":["5471:5480:5482"]},"path":["5482"],"owner":"11","recid":"59690","title":["Approximate Greatest Common Divisor of Multivariate Polynomials and Its Application to III-Conditioned Systems of Algebraic Equations"],"pubdate":{"attribute_name":"公開日","attribute_value":"1991-12-31"},"_buckets":{"deposit":"e57a2d68-54cb-4b8d-8a82-49265efcad71"},"_deposit":{"id":"59690","pid":{"type":"depid","value":"59690","revision_id":0},"owners":[11],"status":"published","created_by":11},"item_title":"Approximate Greatest Common Divisor of Multivariate Polynomials and Its Application to III-Conditioned Systems of Algebraic Equations","author_link":["361491","361490","361487","361489","361488","361492"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Approximate Greatest Common Divisor of Multivariate Polynomials and Its Application to III-Conditioned Systems of Algebraic Equations"},{"subitem_title":"Approximate Greatest Common Divisor of Multivariate Polynomials and Its Application to III-Conditioned Systems of Algebraic Equations","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"（IPSJ Best Paper Award、論文賞受賞）","subitem_subject_scheme":"Other"}]},"item_type_id":"5","publish_date":"1991-12-31","item_5_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Computer Division  Information Equipment  Sector  Matsushita Electric Industrial Co.  LTD."},{"subitem_text_value":"Department of Computer Science  Ehime University"},{"subitem_text_value":"The Institute of Physical and Chemical Research/Institute of Mathematics  University of Tsukuba"}]},"item_5_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Computer Division, Information Equipment  Sector, Matsushita Electric Industrial Co., LTD.","subitem_text_language":"en"},{"subitem_text_value":"Department of Computer Science, Ehime University","subitem_text_language":"en"},{"subitem_text_value":"The Institute of Physical and Chemical Research/Institute of Mathematics, University of Tsukuba","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"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/59690/files/IPSJ-JIP1403009.pdf","label":"IPSJ-JIP1403009"},"date":[{"dateType":"Available","dateValue":"1993-12-31"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-JIP1403009.pdf","filesize":[{"value":"1.1 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"0","billingrole":"5"},{"tax":["include_tax"],"price":"0","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"d82681d3-5295-4b60-b470-0c116db71fcf","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 1991 by the Information Processing Society of Japan"}]},"item_5_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Masa-AkiOchi"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Matu-TarowNoda"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Tateaki, Sasaki"}],"nameIdentifiers":[{}]}]},"item_5_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Masa-Aki, Ochi","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Matu-Tarow, Noda","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Tateaki, Sasaki","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_5_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA00700121","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_5_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1882-6652","subitem_source_identifier_type":"ISSN"}]},"item_5_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"Let F  F and D be multivariate polynomials andεbe a small positive number 0 < ε < < 1. If F=DF+△F  where △F　is a polynomial with coefficients that are O(ε)-smaller than those of F  D is called an approximate divisor of F of accuracy c. Given multivariate polynomials F and G  an algorithm is proposed for calculating with accuracyεthe approximate greatest common divisor (GCD) of F and G. The algorithm is a naive extension of the conventional Euclidean algorithm  but it is necessary to treat the polynomials carefully. As an application of the approximate GCD of multivariate polynomials  the solution of a system of algebraic equations {F_1(x  y  . . .   z)=0 . . .   F_r(x  y  . . .  z)=0} is considered  where F_i and F_j  i≠j  have a non-trivial approximately common divisor. Such a system is ill-conditioned for conventional numerical methods  and is transformed to a well-con-ditioned system by calculating approximate GCD's. A method is also given for determining the initial approximations of the roots for numerical iterative calculation. The proposed method is tested by using several examples  and the results are very good.","subitem_description_type":"Other"}]},"item_5_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"Let F, F and D be multivariate polynomials andεbe a small positive number,0 < ε < < 1. If F=DF+△F, where △F　is a polynomial with coefficients that are O(ε)-smaller than those of F, D is called an approximate divisor of F of accuracy c. Given multivariate polynomials F and G, an algorithm is proposed for calculating with accuracyεthe approximate greatest common divisor (GCD) of F and G. The algorithm is a naive extension of the conventional Euclidean algorithm, but it is necessary to treat the polynomials carefully. As an application of the approximate GCD of multivariate polynomials, the solution of a system of algebraic equations {F_1(x, y, . . . , z)=0,. . . , F_r(x, y, . . ., z)=0} is considered, where F_i and F_j, i≠j, have a non-trivial approximately common divisor. Such a system is ill-conditioned for conventional numerical methods, and is transformed to a well-con-ditioned system by calculating approximate GCD's. A method is also given for determining the initial approximations of the roots for numerical iterative calculation. The proposed method is tested by using several examples, and the results are very good.","subitem_description_type":"Other"}]},"item_5_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"300","bibliographic_titles":[{"bibliographic_title":"Journal of Information Processing "}],"bibliographicPageStart":"292","bibliographicIssueDates":{"bibliographicIssueDate":"1991-12-31","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"3","bibliographicVolumeNumber":"14"}]},"relation_version_is_last":true,"weko_creator_id":"11"},"id":59690,"updated":"2025-01-20T06:33:06.896564+00:00","links":{}}