{"created":"2021-03-01T05:52:59.396095+00:00","id":1274,"links":{},"metadata":{"_buckets":{"deposit":"1994ddc4-77db-4520-89ed-b21ea1d2123e"},"_deposit":{"id":"1274","owners":[],"pid":{"revision_id":0,"type":"depid","value":"1274"},"status":"published"},"_oai":{"id":"oai:repository.nii.ac.jp:00001274","sets":["136"]},"author_link":[],"control_number":"1274","item_5_biblio_info_30":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2013-12-03","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"24","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":"We develop a general convergence theory for the generalized minimal residual method preconditioned by inner iterations for solving least squares problems. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory improves previous work [K. Morikuni and K. Hayami, SIAM J. Matrix Appl. Anal., 34 (2013), pp. 1–22], particularly in the rank-deficient case. We also characterize the spectrum of the preconditioned coefficient matrix by the spectral radius of the iteration matrix for the inner iterations, and give a convergence bound for the proposed methods. Finally, numerical experiments show that the proposed methods are more robust and efficient compared to previous methods for some rank-deficient 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":"10.20736/0000001274","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":"保國, 惠一","creatorNameLang":"ja"},{"creatorName":"Morikuni, Keiichi","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":"2019-03-13"}],"displaytype":"detail","filename":"13-004E.pdf","filesize":[{"value":"452.8 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"NII Technical Report (NII-2013-004E)：Convergence of Inner-iteration GMRES Methods for Least Squares Problems (Revised Version)","url":"https://repository.nii.ac.jp/record/1274/files/13-004E.pdf"},"version_id":"b6cbb07e-5fa5-4bb8-9df0-3dd812f935fb"}]},"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-2013-004E)：Convergence of Inner-iteration GMRES Methods for Least Squares Problems (Revised Version)","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"NII Technical Report (NII-2013-004E)：Convergence of Inner-iteration GMRES Methods for Least Squares Problems (Revised Version)","subitem_title_language":"en"}]},"item_type_id":"5","owner":"1","path":["136"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2019-03-13"},"publish_date":"2019-03-13","publish_status":"0","recid":"1274","relation_version_is_last":true,"title":["NII Technical Report (NII-2013-004E)：Convergence of Inner-iteration GMRES Methods for Least Squares Problems (Revised Version)"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2023-01-11T02:43:29.778511+00:00"}