{"created":"2021-03-01T05:52:09.149396+00:00","id":410,"links":{},"metadata":{"_buckets":{"deposit":"681e8360-27c1-48fb-a285-aab24fcd51f1"},"_deposit":{"id":"410","owners":[],"pid":{"revision_id":0,"type":"depid","value":"410"},"status":"published"},"_oai":{"id":"oai:repository.nii.ac.jp:00000410","sets":["136"]},"author_link":[],"control_number":"410","item_5_biblio_info_30":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2005-10-29","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"20","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"NIIテクニカル・レポート","bibliographic_titleLang":"ja"},{"bibliographic_title":"NII Technical Report","bibliographic_titleLang":"en"}]}]},"item_5_description_28":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"大規模疎なm×n行列Aを係数行列とする最小二乗問題に対する主流の反復法は, 正規方程式に対して(前処理付き)共役勾配法を適用するCGLS法である. 本論文ではまず, 代案として元の最小二乗問題を, n×m行列Bを用いて, 正方行列ABまたはBAを係数行列にもつ等価な最小二乗問題に変形し, 非対称正方行列を係数行列とする連立一次方程式用のロバストなクリロフ部分空間反復法である一般化最小残差法(GMRES)を適用する手法を提案する. 次に, m≧n (優決定), m<n (劣決定), およびランク落ちも含めた一般の場合に対して, これらの手法が任意の右辺項bに対して破綻することなく最小二乗解を与えるための行列Bに関する十分条件を導く. そして, Bの例として不完全QR分解の一つであるIMGS(l)法を提案する. 最後に, フルランクな優決定および劣決定問題に対する数値実験により, 条件の悪い問題では(対角スケーリングに相当する)IMGS(0)法を用いた提案手法の方が従来の前処理付きCGLS法より速く最小二乗解を与えることを示す.","subitem_description_language":"ja","subitem_description_type":"Abstract"},{"subitem_description":"The most commonly used iterative method for solving large sparse least squares problems with an m¡ßn coefficient matrix A is the CGLS method, which applies the (preconditioned) conjugate gradient method to the normal equation. In this paper, we consider alternative methods using an n¡ßm matrix B to transform the problem to equivalent least squares problems with square coefficient matrices AB or BA, and then applying the Generalized Minimal Residual (GMRES) method, which is a robust Krylov subspace iterative method for solving systems of linear equations with nonsymmetric coefficient matrices. Next, we give a sufficeint condition concerning B for the proposed methods to give a least squares solution without breakdown for arbitrary right hand side b, for over-determined, under-determined and possibly rank-deficient problems. Then, as an example for B, we propose the IMGS(l) method, which is an incomplete QR decomposition. Finally, we show by numercial experiments on full-rank over-determined and under-determined problems that, for ill-conditioned problems, the proposed method using the IMGS(0) method, which is equivalent to diagonal scaling, gives a least squares solution faster than previous preconditioned CGLS methods.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_5_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.20736/0000000410","subitem_identifier_reg_type":"JaLC"}]},"item_5_publisher_31":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"国立情報学研究所","subitem_publisher_language":"ja"}]},"item_5_source_id_32":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1346-5597","subitem_source_identifier_type":"ISSN"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"速水, 謙","creatorNameLang":"ja"},{"creatorName":"Hayami, Ken","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"伊藤, 徳史","creatorNameLang":"ja"},{"creatorName":"Ito, Tokushi","creatorNameLang":"en"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2015-08-27"}],"displaytype":"detail","filename":"05-015J.pdf","filesize":[{"value":"309.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"NIIテクニカル・レポート (NII-2005-015J)：GMRES法による最小二乗問題の解法","url":"https://repository.nii.ac.jp/record/410/files/05-015J.pdf"},"version_id":"a0aaba48-5cb4-409a-b66a-b983aeaa01dd"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"テクニカルレポート","subitem_subject_language":"ja","subitem_subject_scheme":"Other"},{"subitem_subject":"Technical Report","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"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":"NIIテクニカル・レポート (NII-2005-015J)：GMRES法による最小二乗問題の解法","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"NIIテクニカル・レポート (NII-2005-015J)：GMRES法による最小二乗問題の解法","subitem_title_language":"ja"},{"subitem_title":"NII Technical Report (NII-2005-015J)：The Solution of Least Squares Problems Using GMRES Methods","subitem_title_language":"en"}]},"item_type_id":"5","owner":"1","path":["136"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2005-10-29"},"publish_date":"2005-10-29","publish_status":"0","recid":"410","relation_version_is_last":true,"title":["NIIテクニカル・レポート (NII-2005-015J)：GMRES法による最小二乗問題の解法"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-12-27T08:34:01.045808+00:00"}