{"created":"2022-06-09T06:56:04.651259+00:00","id":2000372,"links":{},"metadata":{"_buckets":{"deposit":"9a0442f0-df61-4a20-87d1-27378dc01164"},"_deposit":{"created_by":18,"id":"2000372","owner":"18","owners":[18],"owners_ext":{"displayname":"NII","username":"niirepo"},"pid":{"revision_id":0,"type":"depid","value":"2000372"},"status":"published"},"_oai":{"id":"oai:repository.nii.ac.jp:02000372","sets":["136"]},"author_link":[],"control_number":"2000372","item_5_biblio_info_30":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2020-09-10","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"13","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":"In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the authors analyzed the convergence behaviour of the Generalized Minimal Residual (GMRES) method for the least squares problem $ \\min_{x \\in R^n} {\\| b - A x \\|_2}^2$, where $ A \\in R^{nxn}$ may be singular and $ b \\in R^n, by decomposing the algorithm into the range $ R(A) $ and its orthogonal complement $ R(A)^\\perp $ components. However, we found that the proof of the fact that GMRES gives a least squares solution if $ R(A) = R(A^T) $ was not complete. In this paper, we will give a complete proof.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_5_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.20736/0002000372","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":"杉原, 光太","creatorNameLang":"ja"},{"creatorName":"Sugihara, Kota","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":"2022-06-09"}],"displaytype":"detail","filename":"20-004E.pdf","filesize":[{"value":"139 KB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"NII Technical Report (NII-2020-004E)：GMRES on singular systems revisited","url":"https://repository.nii.ac.jp/record/2000372/files/20-004E.pdf"},"version_id":"f86ad040-39e1-4fd6-8ea7-7a95132c5668"}]},"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-2020-004E)：GMRES on singular systems revisited","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"NII Technical Report (NII-2020-004E)：GMRES on singular systems revisited","subitem_title_language":"en"}]},"item_type_id":"5","owner":"18","path":["136"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2022-06-09"},"publish_date":"2022-06-09","publish_status":"0","recid":"2000372","relation_version_is_last":true,"title":["NII Technical Report (NII-2020-004E)：GMRES on singular systems revisited"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2023-01-11T06:02:14.613365+00:00"}