{"created":"2021-03-01T05:52:08.196045+00:00","id":394,"links":{},"metadata":{"_buckets":{"deposit":"8e18af74-8cdf-4ccc-8c58-0027ec2495aa"},"_deposit":{"id":"394","owners":[],"pid":{"revision_id":0,"type":"depid","value":"394"},"status":"published"},"_oai":{"id":"oai:repository.nii.ac.jp:00000394","sets":["136"]},"author_link":[],"control_number":"394","item_5_biblio_info_30":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2004-05-07","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"29","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":"For least squares problems of minimizing || b - A x ||_2 where A is a large sparse m x n (m >= n) matrix, the common method is to apply the conjugate gradient method to the normal equation A^T A x = A^T b. However, the condition number of A^T A is square of that of A, and convergence becomes problematic for severely ill-conditioned problems even with preconditioning. In this paper, we propose two methods for applying the GMRES method to the least squares problem by using a n x m matrix B. We give the necessary and sufficient condition that B should satisfy in order that the proposed methods give a least squares solution. Then, for implementations for B, we propose an incomplete QR decomposition IMGS(l). Numerical experiments show that the simplest case l=0, which is equivalent to B= ( diag (A^T A) )^(-1) A^T, gives best results, and converges faster than previous methods for severely ill-conditioned problems.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_5_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.20736/0000000394","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":"伊藤, 徳史","creatorNameLang":"ja"},{"creatorName":"Ito, Tokushi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"速水, 謙","creatorNameLang":"ja"},{"creatorName":"Hayami, Ken","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":"04-006E.pdf","filesize":[{"value":"363.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems","url":"https://repository.nii.ac.jp/record/394/files/04-006E.pdf"},"version_id":"43aa6a1e-fd58-432a-911c-eb721781dcfa"}]},"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":"eng"}]},"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 Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems","subitem_title_language":"en"}]},"item_type_id":"5","owner":"1","path":["136"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2004-05-07"},"publish_date":"2004-05-07","publish_status":"0","recid":"394","relation_version_is_last":true,"title":["NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-12-27T04:15:05.988071+00:00"}