{"_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", "download_preview_message": "", "file_order": 0, "filename": "20-004E.pdf", "filesize": [{"value": "139 KB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 139000.0, "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"], "permalink_uri": "https://doi.org/10.20736/0002000372", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2022-06-09"}, "publish_date": "2022-06-09", "publish_status": "0", "recid": "2000372", "relation": {}, "relation_version_is_last": true, "title": ["NII Technical Report (NII-2020-004E)：GMRES on singular systems revisited"], "weko_shared_id": -1}